ޥ
ޤޤҤǹˤʤäƤޤޤŤäƤΤԤФ˳Ƥޤޤ...ߥäƤʤɤΤǤ...Ȥ櫓ǡϣˤʤͽǤm(__)m
MacOS X 310ڡ 0:05:38 MAIL:masaru-y@kt.rim.or.jp HomePage:24653
Ϥʤ

ס˥ꥢ륿໲ä飱̤

ˤäƤߤޤ
ϻѷγĺˣֹդ
ΣǷ


ĺɮ񤭡ʣ᣶̤
̡λѷ򣲸ĺ褦˷֡ʣãᣱ̤ꢫɵߥפƤޤãᣱ̤Ǥ͡
ȡ硡 310ڡ 23:59:44 HomePage:http://hanau.daa.jp/blog2/24654
ߥƥ
ĥäƥꥢ륿໲äޤˤ⣲̡
ġʥץ񤤤Ƥᤫʡʤ

100 p=0
110 for a65=0 to 1
120 for a64=0 to 1
130 for a63=0 to 1
140 for a62=0 to 1
150 for a61=0 to 1
160 for a54=0 to 1
170 for a53=0 to 1
180 for a52=0 to 1
190 for a51=0 to 1
200 for a43=0 to 1
210 for a42=0 to 1
220 for a41=0 to 1
230 for a32=0 to 1
240 for a31=0 to 1
250 for a21=0 to 1
310 b1=0
320 b2=0
330 b3=0
340 b4=0
350 b5=0
360 b6=0
410 if a65=1 then b6=b6+1
420 if a65=1 then b5=b5+1
430 if a64=1 then b6=b6+1
440 if a64=1 then b4=b4+1
450 if a63=1 then b6=b6+1
460 if a63=1 then b3=b3+1
470 if a62=1 then b6=b6+1
480 if a62=1 then b2=b2+1
490 if a61=1 then b6=b6+1
500 if a61=1 then b1=b1+1
510 if a54=1 then b5=b5+1
520 if a54=1 then b4=b4+1
530 if a53=1 then b5=b5+1
540 if a53=1 then b3=b3+1
550 if a52=1 then b5=b5+1
560 if a52=1 then b2=b2+1
570 if a51=1 then b5=b5+1
580 if a51=1 then b1=b1+1
590 if a43=1 then b4=b4+1
600 if a43=1 then b3=b3+1
610 if a42=1 then b4=b4+1
620 if a42=1 then b2=b2+1
630 if a41=1 then b4=b4+1
640 if a41=1 then b1=b1+1
650 if a32=1 then b3=b3+1
660 if a32=1 then b2=b2+1
670 if a31=1 then b3=b3+1
680 if a31=1 then b1=b1+1
690 if a21=1 then b2=b2+1
700 if a21=1 then b1=b1+1
800 if (b1-2)^2+(b2-2)^2+(b3-2)^2+(b4-2)^2+(b5-2)^2+(b6-2)^2=0 then p=p+1
810 next a21
820 next a31
830 next a32
840 next a41
850 next a42
860 next a43
870 next a51
880 next a52
890 next a53
900 next a54
910 next a61
920 next a62
930 next a63
940 next a64
950 next a65
960 print p
970 end
310ڡ 0:13:21 HomePage:ߤ24655

դ
äȤ㤤Ǿ٤줿
̤äνƤʵ롣

ȣȤȲꤷ
ʣˤȡʣˤĤŤ֤ȻĤ꤬ޤ
ǣ̤ꡣ
ʣȣˤ֤ȻĤ̤ꡣ
ף̤Ф̤ǣ̤ꡣ
ˡι񡡡 310ڡ 0:15:22 HomePage:¤ο24656
Taro
̤141λѿĤȻͳѿȤʬˤΤ
׻ߥϢȯʤȤˤɤĤޤ

Ϸɥץࡦޤ
ľ塡 310ڡ 0:21:39 24657
ߤ
ޤäƤ륫ɤϰʲΣ硣






ĤΤϣ̤뤬Ȥꤢ
ȣ֤Ȥˤ롣
飵ΤĤɤǾ櫓
ʤˣȣ֢ΤȤԤͤΤԲġ
ʤˣȣȣȣȣΤ줫
줾Фƾ˹פΤ̤ꡣ
ʤϡˣȣ֢ΤȣΤɤ
Ǥ˹פΤ̤ꡣ

ɣߣܣߣߣ᣷̤꤬Ȥʤ롣

ίޤ졡 310ڡ 0:30:47 24658
tomh
ĥĤȿ夲ޤ
äƤɤä (^^;)ۥ
ԡ 310ڡ 0:25:21 MAIL:tomh@yahoo.co.jp HomePage:H to M24659

ɽʤΤäơʤߤ󤵤Τ褦ʤΡˡȤȤʬƿ夲ޤ
˽񤯤ˤϸˤ᤮ʽˤΤdz䰦

ˤƤ⡢Ϥʤβ#24654ä㥷ץ롦줾ϡߤʡ
̤̪ 310ڡ 0:28:20 MAIL:ishizaki@qa.so-net.ne.jp 24660

Total Access = 3620000äơǤɽƶä
ƽ 310ڡ 0:30:55 HomePage:θ줳ߤ󡪡24661
schrodin
Ϥʤġ
310ڡ 0:31:33 24662

#24558
21
3132
414243
51525354
6162636465
Σ̤Ǥ͡
ƽ 310ڡ 0:33:25 HomePage:θ줳ߤ󡪡24663
ߤ
#24663ʷ
ޤäʴˡĹȲˡ񤤤ƤƤߥѤ
򤯤ˤϱƶʤɡ
ίޤ졡 310ڡ 0:38:51 24664
ٶ
#24654
ƱͤǤǤͤϤפĤΤ1֤⤫äƤޤޤ
Ǥͤ͡פ֤Υꥢ륿໲ääΤǡäԤ
ǰǤȡ꤬򤱤Ȥ˴ưޤ褯ǤǤ͡
ǤϤ褦ʤ顣
310ڡ 1:13:05 24665
ҡΤ
ߤͤȤۤƱǤʡ
ǽʬְ㤨400̤ꤰ餤ΤɤǤˤʤäƤޤäʤǤʶ
Ϥʤͤβˡ˴ưäꤷޤʤ
ɥ 310ڡ 1:26:39 HomePage:24666
Taku-chan
10ʬDz򤱤
30ʬ餤ʡ
ͤϡ
ΰ̡ΰ̤Τɤ餫ˣޤޤ륫ɤϣ
ΰ̡ΰ̤Τɤ餫ˣޤޤ륫ɤϣ
ΰ̡ΰ̤Τɤ餫ˣޤޤ륫ɤϣ
ΰ̡ΰ̤Τɤ餫ˣޤޤ륫ɤϣ
ΰ̡ΰ̤Τɤ餫ˣޤޤ륫ɤϣ
ΰ̡ΰ̤Τɤ餫ˣޤޤ륫ɤϣ
ȹͤȡ
ΰ̣5̤߽ΰ̣65ȤϽΰ̣ˤ3̤߻ĤǾ˹礦Τ1̤15̤
ˤʤޤ͡
ȺФɡƱΤޤǤΤϻȤʤ顢
158260̤ꡣ
ˡ213132ȡ546465Τ褦ˡ
6Ĥο椫3Ĥοǡ3ĤȤ߹碌2ĤǽƤΤ
У10̤ꡣ
­70̤ꡦǤƤʤ
310ڡ 1:30:54 24667
Ϥʤ
#24666ҡΤ󡡤
#24665ϡٶ
#24662schrodin
#24660

(ҡ)Ҥ꤬ȤޤĤ䤫ʲˡܻؤƲ򤤤Ƥޤ󤳤ʤդ˥ХäȤФǤɤ͡ƻϸǤ(ء)

ȡ硡 310ڡ 1:58:36 HomePage:http://hanau.daa.jp/blog2/24668
ʤ
򣶳ѷĺˡɤϻѷդгбޤ
ɤο⣲٤ʤΤǡ롼׾ΰɮ񤭤Ƥ뤳Ȥˤʤޤ
Ϥʤ󡢤ۤΤߤʤޤƱǤ
̳ƻ 310ڡ 7:46:45 MAIL:naka@sansu.org HomePage:naka's Home Page24669
Ŵƻ˥ޥʥޥǡ˾
ˤƤϤʤͤ
פĤФäᤫäΤˤʤ
ʤߤ˲ϥ륯ͤƱǤܤߤͤƱäƲ򤤤Ƥޤ
ȤڭҤǤʥޥǡˡ 310ڡ 7:55:31 24670

ǯTORA󤬽ꤷܼŪˤƱߤ
310ڡ 9:05:56 24671
kasama
Ϥ褦ޤ褯ͤˡץˤ餻ޤ(^_^;)

import java.util.*;
public class Question441 {
public static void main(String[] args) {
List numberList = Arrays.asList(new String[]{"12","13","14","15","16","23","24","25","26","34","35","36","45","46","56"});
int count = 0;
for (int n = 1; n <= numberList.size(); ++n) {
List list = new Combination(numberList, n).getList();//Combination#19625
for (Iterator iter = list.iterator(); iter.hasNext(); ) {
List eList = (List) iter.next();
int[] checkNumber = new int[]{0,0,0,0,0,0};
for (Iterator eIter = eList.iterator(); eIter.hasNext(); ) {
String s = (String) eIter.next();
for (int i = 0; i < checkNumber.length; ++i) {
char c = (char)('1' + i);
if ((s.charAt(0) == c && s.charAt(1) != c) ||
(s.charAt(0) != c && s.charAt(1) == c)) ++checkNumber[i];
}
}
boolean flag = true;
for (int i = 0; i < checkNumber.length; ++i) {
if (checkNumber[i] != 2) {
flag = false;
break;
}
}
if (flag) ++count;
}
}
System.out.println(count);
}
}
310ڡ 10:00:20 24672
DrK
ϡɽ˽ФƤʤʤȻפʤ餤ΤǤޤ
70ȤȤǡξϡ3ĤοDzȤ6Ƥν¤ȤȤˤʤޤ
1˹ͤơ3Ĥˡϡ5Ĥο2Ĥ٤ФΤǡ5C2=10
6Ĥονϡ1ˤ5!=120Ȥʤ뤬10ΰ̤1ΰ̤礭ʤΤǡȿиνƱΤȤߤʤ2dz롣
120/2=60
10+60=70
ҡ 310ڡ 12:17:43 MAIL:satoka@star.odn.ne.jp 24673
uchinyan
ϤˤϡϳڤǤ ^^/
⤦ڤߤΤǡ虜ȷǼĤɤޤˡ̲ͤƤߤ褦ȻפäƤޤ
ǤλβˡǤĤζŪʻԺθ˵դޤ
񤫤Ƥγư̤ο 1, 2, 3, 4, 5, 6 Ǥ1 ʳ a, b, c, d, e Ƚ񤯤Ȥˤޤa, b, c, d, e ϰۤʤޤ
񤫤ƤϡͿƤ狼顢ĤοͿȰդޤޤǡ (a,b) ʤɤȽ񤯤Ȥˤޤ
㤨С(1,2) = 21, (6,4) = 64, (1,a) = a1, (d,b) ϡd > b ʤ db Ǥ
ơɤȤơɽܤơ(1,a) -> (a,b) -> (b,c) -> ... Τ褦˽֤֤ȹͤƤդ̷⤷ޤ
ȡ
(1,a) -> (a,1) ξ
Ʊ a1 礷ǤʤΤդޤ󡣤Ȥ̣ޤ
(1,a) -> (a,b) -> (b,1) ξ
ΥɤФ졢1, a, b 󤺤ĸƤΤǡĤο (c,d) -> (d,e) -> (e,c) Ȥʤդޤ
ξϡϻĤοĤȤʬơĤ¤٤硢a 2̤ b ̤ꡢǤ
(1,a) -> (a,b) -> (b,1) (1,b) -> (b,a) -> (a,1) ʤΤȾʬˤޤ
Ĥޤꡢ6C3/2 * 2!/2 * 2!/2 = 10 ̤ꡣ
(1,a) -> (a,b) -> (b,c) -> (c,1) ξ
Ĥο (d,e) -> (e,d) Ȥʤ뤳ȤˤʤޤϣˤξƱǥɤϰ礷Ф줺դޤ
(1,a) -> (a,b) -> (b,c) -> (c,d) -> (d,1) ξ
Ĥο e ʤΤǡɤ٤餫ˤꤨޤ
(1,a) -> (a,b) -> (b,c) -> (c,d) -> (d,e) -> (e,1) ξ
ϻΥɤФ졢1, a, b, c, d, e 󤺤ĸƤΤǡդޤ
ξϡˤξƱͤ˹ͤơ5!/2! = 60 ̤ꡣ
ǡϿԤ줿ΤǽǤ
äơ10 + 60 = 70 ̤ꡢˤʤޤ
ͥνȡ 310ڡ 14:40:50 MAIL:uchi@sco.bekkoame.ne.jp 24674
uchinyan
(ޤ)
βˡ #24674 Ǥѷɮ񤭤ˤʤ褦Ǥ
ĤľˤʤϻĤѰդޤ߼ΰۤʤϻĤͤФǤ礦
1, 2, 3, 4, 5, 6 οդޤơ㤨С12Ȥˡ21פȽ񤫤줿ɤФ줿ȹͤޤ
ξǡְ󤺤̤װɮ񤭤ͤޤ
1ФƹԤä1äƤΤȤޤãƤʤ x ˤϡ
x Ʊͤΰɮ񤭤̤ͤäƤʤʤʤޤǤ³ޤ
ΰɮ񤭤ǤϡɬäƽФƹԤΤǡиȤߤʤޤ
ȡξ礬ͤޤ
1ФƤ٤Ƥ̤ä1äƤ硧#24674 Σˤб
1ʳ¤٤ФΤǤ1ؤνθϰ̣ʤΤȾʬˤơ5!/2 = 60 ̤ꡣ
1Фư̤ä1äƤ硧
Ĥο˽äƼξ礬ޤ
⣱˰ĤäƤ硧#24674 Σˤбդΰɮ񤭤Ω̣ʤ
⣲ĤäƤ硧#24674 Σˤб˴ؤդΰɮ񤭤Ωޤ
⣳˻ĤäƤ硧#24674 Σˤб
Ĥλȹ碌Ȥΰɮ񤭤Ω示ĤΥɤФ졢դޤ
ɮ񤭼Τϸ̵뤹Ф줾̤ǡ1٤ФΤǡ5C2 = 10 ̤ꡣ
⣴˻ĤäƤ硧#24674 Σˤб⣲ˤƱͤǡդޤ
⣵˸ĤäƤ硧#24674 ˤбʤ1ˤʤäƤޤΤạ̇̄ޤ
ʾǽǤ
äơ60 + 10 = 70 ̤ꡣ

ͥνȡ 312ڡ 11:02:00 MAIL:uchi@sco.bekkoame.ne.jp 24675
̾õ
Ȥʤ顢̤
Ȥʤ顢̤
Ȥʤ顢̤
Ȥʤ顢̤
Ȥʤ顢̤
Ȥʤ顢̤
1312704653822,...οο󥵥Ȥ˥ȥꤵƤʤ褦Ǥ
310ڡ 16:41:30 24676
̾õ
Ȥʤ顢̤
Ȥʤ顢̤
Ȥʤ顢̤
Ȥʤ顢̤
Ȥʤ顢̤
Ȥʤ顢̤
1312704653822,...οο󥵥Ȥ˥ȥꤵƤʤ褦Ǥ
310ڡ 17:04:56 24677
̾õ

Ȥʤ顢3507̤
󥵥ȤA001205Τ褦Ǥ
310ڡ 17:21:12 24678
uchinyan
⤦ġǽͤƤƤ󤬤餬äƻߤ᤿ƻʲˡǤ⤦٥ȥ饤ޤ (^^;
βˡ #24674 εˡȤޤ
1 ڤ 6 üǡ(a,1) = a1, (b,1) = b1, (c,6) = 6c, (d,6) = 6d Ȥʤޤa, b, c, d ϡ٤ưۤʤȤޤ
ΤȤξʬǽǤ
a1, b1, 6c, 6d ξ硧
(a,b) and (c,d), (a,c) and (b,d), (a,d) and (b,c) λ̤򤬲ǽǤ
äơa, b, c, d 1 6 ˿ʬʬͤơ4C2 * 3 = 18 ̤ꡣ
a1, b1, 6a, 6d a1, b1, 6c, 6b ξ硧
Ĥο x ȤȡԤ (b,x) and (x,d) Ԥ (a,x) and (x,c) ǽǤ
äơξ碌ơ4 * 3 * 2 = 24 ̤ꡣ
a1, b1, 6a, 6b ξ硧
ͤĤοĤƤޤäƤΤǡȤĤοĤʤդȹ礻Ϥޤ
a1, 61, 6c ξ硧
Ĥο x, y Ȥȡ(a,x) and (x,y) and (y,c), (a,y) and (y,x) and (x,c) ǽǤ
ǡ4 * 3 * 2 = 24 ̤ꡣ
a1, 61, 6a ξ硧
Ĥο x, y, z Ȥơ(x,y) and (y,z) and (z,x) ǽǤ
ϡ4 ̤ꡣ
ʾǤ٤ƤǤäơ18 + 24 + 24 + 4 = 70 ̤ꡣ
ͥνȡ 310ڡ 18:15:53 MAIL:uchi@sco.bekkoame.ne.jp 24679
uchinyan
Ǽġɤߤޤ
#24675ϡϤʤ󡢤ʤ¾γƱ褦Ǥ
θ#24674ϡۤ㴳㤦ȻפޤƱȤߤʤƤΤǤ礦
#24679ϡťäơ֤äƤʤ (^^;
ͥνȡ 310ڡ 18:31:58 MAIL:uchi@sco.bekkoame.ne.jp 24680
Ȥ
̤դݤƽ񤭾夲ȻפäΤ
ɤľ¤٤봶βˡǤ̤10ܲϤǤ
Ƥޤ
褺դǻȤ륫ɤ
21,31,32,41,42,43,51,52,53,54,61,62,63,64,6515
ʲΤ褦ʬ
1ޤ५ɤ{21,31,41,51,61}
2ޤ५ɤ{21,32,42,52,62}
3ޤ५ɤ{31,32,43,53,63}
4ޤ५ɤ{41,42,43,54,64}
5ޤ५ɤ{51,52,53,54,65}
6ޤ५ɤ{61,62,63,64,65}
֥ɤϤ줾ο2Ĥ
ʤΤǾ6
52Ǥ줾10̤ꡦ
{21,31},{21,41},{21,51},{21,61},{31,41},{31,51},{31,61},{41,51},{41,61},{51,61}1
{21,32},{21,42},{21,52},{21,62},{32,42},{32,52},{32,62},{42,52},{42,62},{52,62}2
{31,32},{31,43},{31,53},{31,63},{32,43},{32,53},{32,63},{43,53},{43,63},{53,63}3
{41,42},{41,43},{41,54},{41,64},{42,43},{42,54},{42,64},{43,54},{43,64},{54,64}4
{51,52},{51,53},{51,54},{51,65},{52,53},{52,54},{52,65},{53,54},{53,65},{54,65}5
{61,62},{61,63},{61,64},{61,65},{62,63},{62,64},{62,65},{63,64},{63,65},{64,65}6
ǽϤɤʤǤƱʤΤǺǽ1ʤӤʤκǽ
{21,31}(ȿ{21,41},{21,51},{21,61},{31,41},{31,51},{31,61},{41,51},
{41,61},{51,61}Ʊ̤)(ά)
{21,31,42,53,64,65},{21,31,42,54,63,65},{21,31,43,54,62,65}
{21,31,43,52,64,65},{21,31,43,54,62,65},{21,31,52,54,63,64}
{21,31,53,54,62,64}7̤ꤳȭȤ7*10=70̤ꡦ(
θ˭ԡ 310ڡ 20:56:12 MAIL:nm528@ybb.ne.jp 24681
uchinyan
#24656Υ륯#24658Τߤ󤵤βˡȡβˡ#24679Ȥϡʬλ㤤ޤΤ
Ūʹͤ϶ᤤ褦Ǥ
#24673DrKβˡϡƨƤޤβˡ#24674ȡۤޤƻƤ褦Ǥ
#24667Taku-chanβˡϡϤʤ¾ΰɮ񤭤βˡ˶ᤤǤۤ㤤˶̣Ǥ
ͥνȡ 310ڡ 21:39:58 MAIL:uchi@sco.bekkoame.ne.jp 24682
̾õ
Ϥʤ¾Υդˤˡˤäơ
μबʥΡɤθĿˤΤȤ
ɤΥΡɤ⣲ĤλޤľοƤߤޤ
ʡοϡɮ񤭤Ρɿɽޤ

11!/2=19958400
ȭC(12,3)*8!/2=4435200
ȭC(12,4)*7!/2*3=3742200
ȭC(12,5)*6!/2*4!/2=3421440
ȭ1/2!*C(12,6)*(5!/2)^2=1663200
ȭȭC(12,5)*C(7,3)*4!/2*3=997920
ȭȭC(12,6)*1/2!*C(6,3)*5!/2=554400
ȭȭ1/3!*C(12,4)*C(8,4)*(3)^3=155925
ȭȭȭ1/4!*C(12,3)*C(9,3)*C(6,3)=15400
34944085̤
310ڡ 23:08:31 24683
arijune
㤭ȤҤᤤȻפä顢ʤȤΤ褦˵ƤƤȤäƤorz^ ^;)
ΤäƤ뤫饤äơ
䤤䡢ȹͤޤ衣
Ȥꤢ1cyclic¤Ǥ뤫顢߼ˤդ롣
ȻĤΣΤɤΣȤäƤϤʤʤΤǡ1-4,1-54ȷ֤ȡȤ2-3-6ǻѷ뤷ʤޤ4236ΤŤ˰Ƥ̤ʤΤ4-3ȡ3-5ȤȤ2-6;äƤޤäơŬä3-2or3-6Ȱʤȡ3-2ΤȤ2-6 6-5Τߤդ3-6λƱ͡
ä5C2(1+3*2)=70
̥
311ʶ 1:21:56 24684
̾õ
A001205ξǤ
μबĤΤȤοA(n)
Ƚ񤯤ȡΩĤ褦Ǥ
A(n+1)=C(n,1)*A(n)+C(n,2)*A(n-2)(1)
ȤС
A(6)=C(5,1)*A(5)+C(5,2)*A(3)
=5*12+10*1=70(2)

ޡĤΥΡɤɤ⣲ĤλޤĥդνG(5)Ƚ񤭤ޤ
(2)Ωϡ
Ρɤղä롧
G(5)°ƥաʣĤΥΡɤɤ⣲Ĥλޤijƥѥ
ˤĤơĤޤΤʤ飱Ĥӡ
λޤξˣܤΥΡɤ֤ޤˤꡢG(6)°륰դǤޤ
ˤο5*A(5)̤ꡣ
ѷʬΥ
G(5)°ƥաʣĤΥΡɤɤ⣲Ĥλޤijƥѥ
ˤĤơĤΥΡɤӡΣĤΥΡɤˣܤΥΡɤä
Ρɴ֤ĥ롼סʻѷˤĤޤG(3)°륰)
λѷʬΥΤˡG(5)°륰դ顢
ΡɤʤʤäƥդG(5-2)°뤳Ȥˤʤޤ
ΤϡG(3)°륰դG(5-2)°륰դ򤢤碌ΤʤΤǡ
G(6)°륰դˤʤޤ
ˤοC(5,2)*A(3)̤ꡣ
פȡ(2)ˤʤޤ
Ʊͤεǡ(1)Ωޤ
311ʶ 9:08:23 24685
Ĺ
#24685
A(n+1)=C(n,1)*A(n)+C(n,2)*A(n-2)
ˤĤơ

ƿĤΥ롼פʬƱߤä¤Ǥȹͤޤ礦
㤨n=10ΤȤ
1 2 3

6 5 4
7 8

10 9

11ܤοäƤƤˤƤ餦Ȥˤޤʡ
10̤ꤢޤ͡ɽƤΤC(n,1)*A(n)

㤢C(n,2)*A(n-2)ϲɽƤ뤫ȤȡʡˤǤϺʤѥ
11ܤο¾ο2ĤǻѷĤꡢĤDZߤä¤ǤοǤ
(#24685ɽѹǤ)
311ʶ 14:19:15 24686
Ȼ
ϩ 6!/2+6C3/2 Ǥޤ
311ʶ 12:20:52 24687
uchinyan
#24685
ʤۤɡ̣ɤޤĺޤ
¤ϡ褦ʤȤͤ褦ȤƤΤǤդʬǹԤͤäƤޤ (^^;
󼨤Ƥˤϡդʬ䤬˴ޤޤƤꡢʤȴǤ
ʤΤȤǼĤ󼨤Ƥˡϡť #24679 ʳϤ٤ơ
ɽϰ㤤ޤɮ񤭤βˡѴǽʤ褦Ǥ͡
ͥνȡ 311ʶ 12:52:54 MAIL:uchi@sco.bekkoame.ne.jp 24688
̾õ
#24685 ޤ

A001205ξǤ
μबĤΤȤοA(n)
Ƚ񤯤ȡΩĤ褦Ǥ
A(n+1)=C(n,1)*A(n)+C(n,2)*A(n-2)(1)

(1)Ωϡ
ޡθĤΥΡɤɤ⣲ĤλޤĥդνG(n)Ƚ񤭤ޤ
G(n+1)°륰դˤơ(n+1)ܤΥΡ
G(n)°륰դϤʤΡɡˤϡ
ʣ˰ɮ񤭤룴ʾΥΡɤΤҤȤĤǤ뤫
ʣ˰ɮ񤭤룳ĤΥΡɤΤҤȤĤǤ뤫
Τ줫Ǥ
ʣˤˤĤƤϡĤˡޤ
Ρɤղä롧
G(n)°ƥաnĤΥΡɤɤ⣲Ĥλޤijƥѥ
ˤĤơnܤޤΤʤ飱Ĥӡ
λޤξ(n+1)ܤΥΡɤ֤ޤ
ˤοn*A(n)̤ꡣ
ʣˤˤĤƤϼˡޤ
ѷʬΥ
ĤΥΡɤΤΤʤ顢ĤΥΡɤӡΣĤΥΡɤ
(n+1)ܤΥΡɤäΡɴ֤ĥ롼סʻѷˤĤޤ
ơĤݣĤΥΡɤG(n-2)°륰դ򤹤٤ƤĤޤ
ˤοC(n,2)*A(n-2)̤ꡣ
äơ(1)Ωޤ
311ʶ 12:47:12 24689
uchinyan
ɤƱʤΤǤʹͤ⤢ޤ͡ǼĤ˽񤭹ߤʤ褦ʤΤǡǰΤᡣ
ۤϡ#24667Taku-chan˶᤯ɮ񤭤ˤᤤΤʡ
Ūʷ׻ϡ#24656Υ륯#24658Τߤ󤵤#24681ΥȤ⤵˶ᤤ
ȤβˡǤ

ɤˤϾ2ο񤤤ƤΤǤ
ʬ򤷤ơ1 6 ޤǤοĤĤ줾˽񤫤줿6礬Ȥޤ
ȡͿ줿狼顢ΥɤȤۤʤ2֤ȸΥɤοդ˷Ǥդ⤤ơ
Υɤ˽񤫤줿ȿɤΰۤʤĤȹ礻ϡабޤ
ǡʹߤϡ1 6 ޤǤο񤫤줿ɤȤȹͤޤ
ξ硢դξϴñˤʤäơΥɤȤ2ȡ1 6 ޤǤο񤫤줿ɤ2示Ĥ뤳Ȥ̣ޤ
ȡ12礫ȹ礻οС줬ˤʤޤ
1 Ȥ߹碌ϡ 1 Ф5̤ꡢ⤦Ф4̤ꡢǤ
ʣΤȾʬˤơ5 * 4 / 2 = 10 ̤ꡣ
ǡa1, b1, a > b ǤȤȡο c, d, e (2Ȥ뤳Ȥ)Ȥơ
ab ڤ c, d, e ȹ礻ξ硧c Ф2̤Ǥc ĤΤȾʬˤʤäơ 2/2 = 1̤ꡣ
ab 餺 c, d, e ȺȤ߹碌硧
a c, d, e Ȥȹ礻3̤ꡣb c, d, e Ȥȹ礻ϡa ƱΤȤ߹碌ȸ夬ǤʤΤ2̤ꡣ
Ĥȹ礻2̤ꡣc, d, e 2Ȥ뤳ȤȾʬˤʤäơɡ3 * 2 * 2 / 2 = 6̤ꡣ
äơΤǡ10 * (1 + 6) = 70̤ꡣ
ͥνȡ 311ʶ 14:54:39 MAIL:uchi@sco.bekkoame.ne.jp 24690
X
դ֤󤤤򤷤ƶϫɷ׻ϣʣܣˡ᣷Ǥऺ٤ʬषƹͤޤ
311ʶ 16:16:26 24691
uchinyan
2005/03/12ʤǽξϴְäƤޤޤ

#24690βˡϡ¤ϡ#24688ǼԤȸäؤΥȥ饤ʪǤ
ͤľơA(n+1) = C(n,1) * A(n) + C(n,2) * A(n-2) #24690ή˾Ƥޤ

#24690̲ȡ1 (n+1) ޤǤοĤĤ줾˽񤫤줿 (n+1) Ȥ2Ȥ뤳Ȥˤʤޤ
1 ʳa, b, c, d, e, ..., a > ba > c Ȥޤ
A(n+1) ϡ(n+1) Ĥ 1, a, b, c, d, e, ... οȤ2Ȥ顢 (n+1) Ĥοοˤʤޤ
Ūˤ a, b, c, d, e, ... 1 ɲäФΤǤʲǤϡ#24690򾯤ɤơΤ褦˹ͤޤ
a1, b1, ab ڤ c, d, e, ... ȹ礻ξ
ޤ1 a, b Ȥȹ礻ϡn(n-1)/2 = C(n,2) ̤ˤʤΤǡa1, b1, ab C(n,2) ̤ꡣĤ (n-2) Ĥ A(n-2) ̤ꡣ
äơC(n,2) * A(n-2) ̤ꡣ
a1, b1 ab 餺 c, d, e, ... ȺȤ߹碌
1 ʬ A(n) ٤ʤΤǤab ʤΤǡɬפޤ
A(n) ˤơƤ n ĤοΤĤФ ab Ȥޤ
äơˡa1, b1 ɲäФ櫓Ǥ줬Ȥˤʤޤ
ΤȤξοο񤷤ԤƤޤ (^^;
ϡäʣǤΤ褦ʡ֥ȥåפԤФ褦Ǥ
a ϡA(n) ǡ¾ο ab ʳοĺäƤޤο c ȤäƤ ac Ȥޤ
Ǿο뤿ˡac Ф c1 Ȥ1:1бޤ
ȡ1:1бˤäơa1 ʳϡ1, b, c, d, e ... n ĤοǹƤ뤳Ȥˤʤޤ
ΤȤξοϡa1 ʳ A(n) ̤ꡢa1 a C(n,1) ̤ꡢ C(n,1) * A(n) ̤ˤʤޤ
ʤʤºݤ˹ϡc1 ac ֤ΤʤΤա
)ڤӣˤ顢ɡξ碌ơA(n+1) = C(n,1) * A(n) + C(n,2) * A(n-2) ˤʤޤ

ľäơäȤ䤳Ǥ̾õ夵#24689Ӥȡ
ˤϡʣˤΡ֣ѷʬΥפʬˤϡʣˤΥΡɤղäʬбޤ
ͥνȡ 312ڡ 14:12:04 MAIL:uchi@sco.bekkoame.ne.jp 24692
n
ޤǤˤäƤȤʤȤưڽ񤭤˵
̲񤳤Ȼפä⤦Ǥ˽ФƤޤ

311ʶ 21:13:06 24693
ۤ
Ϥʤ󤿤βˡ˵ĤޤǤФ餷Ǥ

ϼΤ褦˹ͤޤ
1,1,2,2,3,3,4,4,5,5,6,6ΥɤѰաΥɤȤ߹碌ޤ
36ʤ顡63ˤ櫓Ǥ

21ȤäĤΤϡ2,3,4,5,6Τ飲ǡ4C2=10̤
ȤС1硡2,3ȤäĤȤ
ΤΥ2,3,4,4,5,5,6,6ΤäĤͤޤ

23äĤ
ĤΥɤΤäĤ4-54-65-6Σ̤
23줾ۤʤȤäĤ
2ȤäĤ3̤ꡡ3ȤäĤϣ̤ꡡǡ6̤
ȤС2435äĤȤ
Ĥοϡ4566ȤʤꡡĤΤäĤϡ4-65-6ʤ

ʾ夫顡10C2 (1+32)=70̤ꡡȤʤޤ
̤αȡ 312ڡ 16:12:15 MAIL:micci@sansu.org HomePage:ߤäα24694
X
錄Ϥ줾ΥɤŤġŤġŤĤλɤʤΤ줳ͤƤޤޤͤǤλ1-2-3-4-5-6-1ΰɮ񤭤ξϤ⤦ɮ񤭤1-3-5-2-6-4-1Ƥʤʤ³ʤDz̤äƤ줳ͤƤޤ
313 0:05:25 24695
uchinyan
#24695
¤ϻ褦ʤȤ򾯤פäΤǤޤϡɤΤ褦˳ĥΤ򤤤̣ꤽ
򸫶ˤɬפ뤫ʤȻפäƤޤ
ɤ˽񤫤Ƥ2˸¤ꡢȤ 1 6 ˸¤ʤСΤ褦ʤȤʬޤ
Ȥ򡢰1, ..., n Ȥޤɤ˽񤫤Ƥϡ2˸¤Ȥޤ
ξ硢񤫤Ƥϡ21, 31, ,,., n1, 32, 42, ..., n2, ..., n(n-1) Ȥʤޤ
äơդ餫οޤޤ륫ɤ k Ȥȡ1 <= k <= n-1 Ǥ
k ΤȤξο A(n,k) Ȥޤ
餫ˡk = n-1 ξϡ٤ƤΥɤ A(n,n-1) = 1 ̤ꡣ
ޤk >= n ʤСA(n,k) = 0 Ǥ
̤ A(n,k) ξϡݤäΤǤȹͤƤޤ󤬡
ʤȤ⡢k ξɤ򡢤٤ƤΥɤäĤΥɤͤȡ
٤ƤΥɤ n-1 ʤΤǡ줫 k ξȤˤʤꡢ(n-1-k) ξбޤ
󡢵դ⤤ޤ
㤨СβǤ 21, 31, 42, 53, 64, 65 Фơ41, 51, 61, 32, 52, 62, 43, 63, 54 ͤСk = 3 ޤ
#24695䣴λ1-2-3-4-5-6-1ΰɮ񤭤ξϤ⤦ɮ񤭤1-3-5-2-6-4-1
ϡk = 1 51, 42, 63 <---> k = 4 21, 32, 43, 54, 65, 61, 31, 53, 52, 62, 64, 41 Ǥ
Ĥޤꡢk ξ (n-1-k) ξϣбƤꡢA(n,k) = A(n,n-1-k) Ǥ
ξ n = 6 ˸¤ȡ
* k = 1 : A(6,1) = 15 ̤ꡣ#24667Taku-chanη̤ΰ
* k = 2 : A(6,2) = 70 ̤ꡣǤ
* k = 3 : A(6,3) = A(6,5-3) = A(6,2) = 70 ̤ꡣ
* k = 4 : A(6,4) = A(6,5-4) = A(6,1) = 15 ̤ꡣ
* k = 5 : A(6,5) = 1 ̤ꡣ
* k >= 6 : A(6,k) = 0 ̤ꡣ
Ȥʤޤ
դΰɮ񤭤бΤϡk ξϡ k/2 ̤ȹͤΤǤ礦
k ΤȤ񤷤(ΤޤޤǤԲǽ)ʵޤ
ʤA(n.k) ΰ̤ξ硢¿ʬϡޤͤƤޤ
ޤγĥ⡢ɤ˽񤫤줿2˸¤ʤȤΤ⤢ꤽǤ
̤ξ񤷲᤮Ǥk ξϡʬ뤫⤷ʤʡȻפޤ
ФͤƤʤΤǡ

ͥνȡ 313 14:11:42 MAIL:uchi@sco.bekkoame.ne.jp 24696
uchinyan
#24692
䣲a1, b1 ab 餺 c, d, e, ... ȺȤ߹碌
ΤޤޤǤְäƤϤʤΤǤΤ褦ˤнʬǤ (^^;
㺣A(n) ˤơƤ n ĤοΤĤФ ab Ȥޤ
㤳äơˡa1, b1 ɲäФ櫓ǤˤäơA(n) Ѥޤ
㤽ǡab ֤Τ C(n,1) ̤ʤΤǡC(n,1) * A(n) ̤ꡣ
֤ȴñˤʤޤ

#24696
θ塢֤ʤƹͤƤʤΤǤ㤨С2ǡn, k ξˤϡ򤬤ʤǤ͡
ͥνȡ 315ʲС 13:42:53 MAIL:uchi@sco.bekkoame.ne.jp 24697
оϩ
ʬƹͤޤ
ˣء١أڣΤȤ
ء١ڤȡĤΣĤϷޤꡢ4*3*2=24Ȥ
ˣء١ڣףΤȤ
ء١ڤȡĤΣĤϤ줾Фƣ̤ꤢ롣
äơ4*3/2*3=18Ȥ
ˣءأΤȤ
ؤȻĤޤΤǡ4Ȥꡣ
ˣء٣ΤȤ
ء٤ȻĤΣĤϤ줾Фƣ̤ꤢ롣
äơ4*3*2=24Ȥꡣ
24+18+4+24=70Ȥ

ˤ36̤ȻפǤϻǺǤޤʴ
γ 315ʲС 17:53:48 MAIL:pctakada@mail.goo.ne.jp HomePage:Ĥ줭24698
Revin
(i)a-b-c-d-e-fǰѥ
6ĤοʤΤ5!/2=60̤

(ii)a-b-c d-e-f2Ĥǰѥ
3ߤ2ĺΤ6C3/2=10̤

­70̤
Dz򤭤ޤ
315ʲС 20:23:21 24699
ȥȥ
äȤǤ
#24698оϩƱǤˤȤƤޤ
ʼ˸лԡ 315ʲС 23:47:47 MAIL:h-sakai@zb3.so-net.ne.jp 24700