٥륯åĥ
礭Τ1ܡ2ܡ3ܤΤɤǾʬ
1־ͤɤˤ뤫Ǥ줾첿̤꤫Ĵ٤餽줾51419̤ꡣ
5+14+19+14+557
218ڡ 0:12:21 44172

(6C1-1)+(6C2-1)+(6C3-1)+(6C4-1)+(6C5-1)
218ڡ 0:13:56 44173
Ȥ
Basica,b,c,d,e,f¤٤

FOR a=1 to 6
FOR b=1 to 6
if b=a then goto 50
FOR c=1 to 6
if c=a or c=b then goto 40
FOR d=1 to 6
if d=a or d=b or d=c then goto 30
FOR e=1 to 6
if e=a or e=b or e=c or e=d then goto 20
FOR f=1 to 6
if f=a or f=b or f=c or f=d or f=e then goto 10
if a>b AND b<c AND c<d AND d<e AND e<f then let s1=s1+1
if a<b AND b>c AND c<d AND d<e AND e<f then let s2=s2+1
if a<b AND b<c AND c>d AND d<e AND e<f then let s3=s3+1
if a<b AND b<c AND c<d AND d>e AND e<f then let s4=s4+1
if a<b AND b<c AND c<d AND d<e AND e>f then let s5=s5+1
10 next f
20 next e
30 next d
40 next c
50 next b
60 next a
print s1;"+";s2;"+";s3;"+";s4;"+";s5;"=";s1+s2+s3+s4+s5
END

f9ơ5+14+19+14+5=57()
˭ԡ 218ڡ 0:35:37 44174
Mr.ǥ
٥륯åĥΡ#44172ιͤǡܤϡʤƱ
(6C1-1)+(6C2-1)+(6C3-1)+(6C4-1)+(6C5-1)
Ǥ
218ڡ 0:29:06 44175
ǯ
¤٤Ƥơذưȹ碌ޤ
ĤΰưʣȤˡĤΰưʣȤˡĤΰưʣȤˡĤΰưʣȤˡĤΰưʣȤ
ףȤ
218ڡ 0:35:52 44176

Фϡ
ؤؤ̲ФꤷƤޤ(^^;
ؤι⤵123456Ȥ
٤ʤȤ2Ĥοδ֤ˤ1ĤˤĤ
ꦦ2̤֤ͤ(¾Ϥɤ餫ˤ¤٤ʤ)Τ
52^0+42^1+32^2+22^3+12^4=57̤
̲ƤƤߤޤ(>_<)

218ڡ 0:40:02 44177
kyorofumi
Pn+1 = 2*Pn + n, or
Pn = sum[(n,k)-1]{k = from 1 to n-1}

Pn = 2^n - n -1
218ڡ 0:55:28 44178

ˣ¤١
礭Τ򣱤ư礷פ̤ꡢǽ餷Ф餯äΤǥȥ֥Ǥ⤢äʤȼʻפߤ򤷤Ƥޤ
󤬷ǼƤäȣưưȵդޤ
Ϻꡡ 218ڡ 1:07:32 44179
⡼ޥ
äȤɤä ^^;

62^5-1
52^4-1
42^3-1
32^2-1
22^1-1
=2^6-2-5=64-7=57
¨ ^^;v 218ڡ 1:07:46 44180
ϥ饮㡼ƥ
Ϥ褦ޤ

MATLABˤ褯SCILABˤץǤ
218ڡ 3:06:19 HomePage:湩ؤ˥44181
Mr.ǥ
롢Dz̲פĤޤ

ؤ㤤ˡ 1.2.3.4.5.6 Ȥ
{1.2.3.4.5.6}򣲤Ĥʬ 줾㤤¤٤ȹͤ
νϡ{1.2.3.4.5.6}ʬ硡2^6̤ˤΤ
{1} {1,2} {1,2,3}{1.2.3.4.5.6} Ρ6+1̤ŬʤΤ
͡2^6(6+1)57̤

ιͤǤȡͤξǤ⡡2^(+1)̤ꡡǰȯǤ
218ڡ 11:16:27 44182
???
Sub Macro1()
Cells(1, 1).Value = 0
Call saiki(1)
End Sub
Sub saiki(ByVal n As Integer)
Dim deta As Integer, j As Integer
a(n) = 1
While a(n) <= 6
If onaji(n) = 0 Then
If n < 6 - 1 Then
Call saiki(n + 1)
Else
a(6) = 6
For j = 1 To 6 - 1
a(6) = a(6) + j - a(j)
Next j
deta = 0
For j = 1 To 6 - 1
deta = deta - (a(j) > a(j + 1))
Next j
If deta = 1 Then
Cells(1, 1).Value = Cells(1, 1).Value + 1
For j = 1 To 6
Cells(Cells(1, 1).Value, j + 1).Value = a(j)
Next j
End If
End If
End If
a(n) = a(n) + 1
Wend
End Sub
Private Function onaji(ByVal n As Integer) As Integer
Dim j As Integer
onaji = 0 : j = 1
While onaji = 0 And j < n
If a(j) = a(n) Then
onaji = 1
Else
j = j + 1
End If
Wend
End Function
218ڡ 8:35:55 44183
̴
⤤㤤ν¤ְȤϡ56,46,36,26,16ꡢơ1,2,4,8,16̤ʤ롣棲ο¤Ǥ͡ꤹȡ45,35,25,15Ȥ1,2,4,8̤ꡢ34,24,1423,1312ơƱͤ˷׻31+15+7+3+1=57Ȥʤޤ
ٻΤ桡 218ڡ 8:41:50 44184
ǯ
餷ΤȤǤϤޤ#44176򾯤
ưȡưǤοͤ롣
ư־2ξ硢¾3,4,5,6̵ͭʤΤǡưȤ߹碌2^4ưǤ֤1ꡣ
ư־3ξ硢¾4,5,6̵ͭʤΤǡưȤ߹碌2^3ưǤ֤2ꡣ
ư־4ξ硢¾5,6̵ͭʤΤǡưȤ߹碌2^2ưǤ֤3ꡣ
ư־5ξ硢¾6̵ͭʤΤǡưȤ߹碌2^1ưǤ֤4ꡣ
ư־6ξ硢¾οϤʤΤǡưȤ߹碌2^0ưǤ֤5ꡣ
פǡ1*2^42*2^33*2^24*2^15*2^057
ʲäٶˤʤǤ

218ڡ 9:54:47 44185
ˤ
٤ޤ(*_*)
6C1-1+6C2-1+6C3-1+6C4-1+6C5-1
nĽܤ6-nĽ¤Ӥ鴰ܤ­ޤ
ʬŤ餯Ƥʤ
218ڡ 11:56:48 MAIL:nikotan@fat.coara.or.jp 44186
uchinyan
Ϥˤϡơϡ
ϡɤ򸫤ȤޤȤƤɸŪסϢˤϰסǤ礦
γˤΨ㤤褦Ǥ鸫Ƕϫͤ¿Τñʤ뤦äߥʤΤǻʡ
Ĥβˡͤޤξʤˡǡʴ

DZȤʤȤʺȤȤˤޤ
ʺκȱǿͤʬΤǡ 0 ͤޤ 2^6 = 64 ̤ ǡ
ȱǤϤ줾㡼Ȱդ¤֤Ȥˤʤޤ
ˤϡ 0 ͤޤʺʤ礬 1 + 5 + 1 = 7 ̤ꤢΤǡ
οϡ64 - 7 = 57 ̤ꡤȤʤޤ

ʺΰ֡Ẹ¦οͿǾʬ򤷤ơ
(6C1 - 1) + (6C2 - 1) + (6C3 - 1) + (6C4 - 1) + (6C5 - 1) = 5 + 14 + 19 + 14 + 5 = 57 ̤ꡤ
ǡa(n+1) = a(n) * 2 + na(2) = 1a(3) = 4a(4) = 11a(5) = 26a(6) = 57 ̤ꡤ
ȤǤ⤤Ǥ͡
219ʶ 13:11:13 44187
Τ
ߤĤ֤Ǥ٤Ƥξͤޤ
̧̻ԡ 218ڡ 14:06:55 44188
uchinyan
ǼĤɤߤޤ


ʲεҤϡ⤽ϻ伫ȤٶΥ˲᤮ʤΤǤ
޳ѤʤΤǤͤޤǤˤȻפäƸΤǤ
Ȥ⤢äơˡʬϻ F.A.Q. ΡֻϰϡפεҤ򻲹ͤˡ
ĿͤǤиǼŪ˹ԤäƤΤǤäơҴŪʤΤǤϤޤ
ޤǤ⤴ͤǤ餺

(ʤȤˡĤ㤤äΤǡޤ)
ʹͤä򤤤Ǥ

#44172#44173#44175#44178#44186#44187Σ
DZȤʤ֡Ẹ¦οͿǾʬ򤷤ƹͤˡ

#44176#44185#44179(¿ʬ)
123456 餤Ĥ˰ưդ¤Ӥȹͤˡ
ϻפդޤǤ

#44177#44190
٤ʤ褦¤դ¤Ӥȹͤˡ
ä­ȡ٤ʤĤο¤ӤФơ
δ֤ο㤨С63 ʤ 4 5ʤɡ򺸱˿ʬȹͤơ
2132435465 ϡ줾줬 2^0 ̤ꤺĤǡ5 * 2^0 ̤ꡤ
31425364 ϡ줾줬 2^1 ̤ꤺĤǡ4 * 2^1 ̤ꡤ
415263 ϡ줾줬 2^2 ̤ꤺĤǡ3 * 2^2 ̤ꡤ
5162 ϡ줾줬 2^3 ̤ꤺĤǡ2 * 2^3 ̤ꡤ
61 ϡ2^4 ̤ǡ1 * 2^4 ̤ꡤ
Ǥ٤ƤʤΤǡιסȤȤΤ褦Ǥ
פդޤǤ
#44176#44185ȼƱǤȯۤʬ㤤ޤ͡

#44178#44187Σܡ#44196#44197
ˤˡ

#44180#44192
DZȤʤȤκ¦οǾʬ򤷤ƹͤˡ
פդޤǤ

#44184#44195
DZȤʤȤ¤ǾʬĴ٤ˡ
äȴ㤤䤹ΤǤ1 ֹ⤯ 6 㤤ȹͤ褦Ǥ
⤷ϡ⤤㤤˴ؤȤϵս¤֡ȹͤ롤Ǥ⤤Ǥ͡
ǤοѤޤ
פդޤǤ
#44176#44185ȼƱˤʤޤȯۤʬ㤤ޤ͡

#44182#44187κǽ顤#44194
DZȤʤȤǣȤʬդʤ¤Ӥȹͤˡ

#44188
ƻ˿ˡ

#44174#44181#44183
ץˤˡ
219ʶ 14:18:26 44189

#44189
uchinyan
#44177ˤĤơ⤯ꤢ꤬Ȥޤ
Ƥޤm(__)m
­Ĥ꤬٤ʤäƤޤޤ
ñˡ
㤨uchinyan̿̾줿ʺˤĤơ
ʺ52ΤȤ52δ֤34ϡʺꦦɤƤ褯
¾1Ϻ¦6ϱ¦ˤ¤٤ʤΤ
3,4ˤĤƳ2̤2^2̤ꡢȤȤǤ
ʺ63Ǥ4,5ƺ2̤ǡ1,2Ϻ¦ˤ¤Ӥޤ
äʺ41,52,63Ϥ٤2^2̤ȤƳ뤳ȤǤޤ
äǤޤꥹޡȤȤϤʤǤ(^^;

218ڡ 15:34:47 44190
uchinyan
#44190Jޥޤ
ܤ򤢤꤬Ȥޤ
βä褦Ǥ͡褫äǤ
218ڡ 16:26:07 44191
⡼ޥ
#44189 uchinyan ޤ ^^
٤ʤΤǡ^^;
1ϤɤäƤ⺸¦θˤʤʤΤǡ
6155ĤοϺˤ櫓羮ϰդ˷Τǡ2^5
6α¦ˤϺ1ĤʤȤʤ-1
5ϡ14ޤǤ(5礭(ξ6)ϱü˰դ¤٤) 2^4
5α141ɬפʤΤǡ-1
ʲƱͤ˹ͤޤ^^;

¤ˡϰȯǵΤǤǤ͢
ˤͤʤΤ錄μǤ ^^;v Orz
¨ ^^;v 218ڡ 16:26:10 44192
uchinyan
#44192⡼ޥ󤵤
ܤ򤢤꤬Ȥޤ
ɤβϴְäƤ褦Ǥʤ
Ƥޤ
218ڡ 16:55:46 44193
ۡॺ
ϤܤζʾοǤDz򤯤Τ20ʬäƤޤޤޤʲ2^6-(5+2)Ǥ䡼äѤعǶʾοȤɤǤ͡
٥ȥ꡼ȡ 218ڡ 17:48:36 44194
̴
uchinyan
#44184ι̴ǤʬˤǶ̻ˤǤޤ
⤤㤤Ȥ߹碌56ξ硢¤564321ΰġ46ξ硢
465321,546321ġ36ξ硢365421,536421,436521,543621λͤ
ȸͤ˹ͤƤȡ棲οˤʤΤǡ¾ξ
ǤΤ褦ʲˡ񤭹ߤޤ
ٻΤ桡 218ڡ 22:02:27 44195
ϺĹ
Ͽĥäפ֤äΤǡǽ6C1ȤǻϤ᤿ɡ櫓ʬʤʤꡢDz򤳤ѹa(2) = 1a(3) = 4a(4) =10a(5) = 28Ȥޤϳ졢ְ㤤ꡢ
̡a(n+2)=2*(a(n+1)+a(n))Ȥʤ롣ʤa(6)=76Ǵְ㤤ʤȡο𤷤Ƽǧڡä줧
Τ򸫤ٶޤ
ȯʤäɡ͡
219ʶ 11:35:53 44196
ǯ
#44178, #44187κȽޤ󤬡Τ褦ʹͤ򸫤Ĥޤ
nͤξn+1ܤΰ礭ʿͤä롣äϼ3ʬǤ롣
nͤϽ֤¤Ǥ롣n+1ܤֽϡ0n-1ΰ֡nȤ
nͤǤǤ˾̤¤ǤP(n)Ȥˡָ¤֡P(n)Ȥ
nͤǤǤ˾̤¤ǤP(n)Ȥˡ꺸οͤ⤤֤μ¤٤P(n)Ȥ
פǡP(n+1)2*P(n)n
¾ˤΤǤ礦

219ʶ 14:05:43 44197
uchinyan
#44195̴
ܤ򤢤꤬Ȥޤ
ɤβϴְäƤ褦Ǥʤ
Ƥޤ
äȴ㤤䤹ΤǤ1 ֹ⤯ 6 㤤ȹͤΤʡ
⤷ϡ⤤㤤˴ؤȤϵս¤֡ȹͤ롤Ǥ⤤Ǥ͡
ǤοѤޤ
ɤʤǤ礦
219ʶ 14:19:36 44198
uchinyan
#44197ǯԤ
ʤȤϤιͤƳޤ
219ʶ 14:20:18 44199
̴
uchinyan
44198βɤ⤢꤬Ȥޤˤä̤
ǡʤѤƤꡢǤ͡
uchinyanͤ񤭤ˤʤäƤäͤˡֹ⤤Τ򣱡
㤤Τ򣶤פޤ
ٻΤ桡 219ʶ 20:47:54 44201
ˤ⡼
#44176Ʊ褦ˡǿ夲Ʋޤ
㤤Τ򣱡ֹ⤤Τ򣶤Ȥơ¤٤
ưοǾʬޤ

ʲȯۤꡢٶˤʤޤ
220ڡ 16:37:38 44202
ˤ⡼
ľǺ뤦äƤ뤫⤷ʤɡ
äƲ򤤤Ƥߤޤ

ͤդ¤f(n)Ȥ롣
ˣͤؤι⤤ͤ򣱿ơf(n+1)Ĥˡͤ롣

i)nͤ¤դ
οͤäƤդսϡΣ
ؤι⤤¦ο͡פȡؤ㤤¦ο͡פδ֡ᣱ
ͤ¤Ӥΰֱᡡ

סf(n)̤ꡡĭ

ii)ͤؤ㤤¤Ǥ
ʤĤޤꡢͤǤդƤʤ
դˤοͤΤ
ֺ¦οͤκ¦ܤ˹⤤ͤκ¦
ʰֱˤʤˤĤޤ

ס̤ꡡĭ

ܭꡢf(n+1)=2f(n)+n

f(1)=0 f(2)=1ʤΤ
f(3)=2*1 +2=4
f(4)=2*4 +3=11
f(5)=2*11+4=26
f(6)=2*26+5=57
ʾ
224ʿ 22:09:18 44203
ˤ⡼
#44197Ʊäʣߤޤ
224ʿ 22:12:25 44204