Ф󡪡äơ
71ڡ 0:06:03 23171
ԤԤΡά
Ͽʬ˲ˡʬⲿΤ(10,[5])-5*(6,[5])=222
ʤȤ򤿤ƤƤޤΤᤵ˿ʬäƤͤ
ȤäơäȽ񤭴ְ㤤˵Ťޤ[5][4]ˡ

ͤȤƤϸ޳ѷгդιפ10ܤʤΤǤ4֤(10,4)
ǡȤϰĤĺФƤܤʬ6ܤ4־ο(6,4)ʤΤǡ
ο(10,4)-5*(,6,4)=135

ʡˤϣ෸Ǥ
̤̪ 71ڡ 0:20:59 MAIL:ishizaki@qa.so-net.ne.jp 23172

71ڡ 0:21:06 23173

ʤ󤫤
71ڡ 0:23:01 23174
ԤԤΡά
٤ФʤʺǤȤޤ

ޥ뤵ϺʣˤʤΤǤ礦ȤʣˤäΤǤ礦
ϤȤ⤢졢СʤˤΤǤȤ¤ޤm(_ _)m
̤̪ 71ڡ 0:24:21 MAIL:ishizaki@qa.so-net.ne.jp 23175
ޥ
#23172
ꤷϤޤˤȤʤʤǤ֣̤פȤ䤿¿ʤʪ...ˤΤ˵ˤʤäƤޤࡢפʤ...

#27175
ȡǤФˤʤޤ(^^;;
MacOS X 71ڡ 0:27:34 MAIL:masaru-y@kt.rim.or.jp HomePage:23176
CRYING DOLPHIN
125ˤʤ뤫̤ڤǤ#23712β򸫤ơ
135꾯ʤʤȤФޤ
ȿϾԤ
ǯԥ奦ȡ 71ڡ 0:32:52 HomePage:θ³äƤɤΤ餤23177
ԤԤΡά
#23178 (ޥ뤵
AEޤǤȤȡʲΤ褦ʶΤ⥪åʤΤǤ礦
A-B B-C C-A D-E
줬ܤʤ130̤Τ褦ʵ⡦
̤̪ 71ڡ 0:34:36 MAIL:ishizaki@qa.so-net.ne.jp 23178
ޥ
ޤä...ѷʬξ礬ä...

Ϣ³ΥߥˤʤäƤޤޤ...m(__)m
MacOS X 71ڡ 0:35:01 MAIL:masaru-y@kt.rim.or.jp HomePage:23179
CRYING DOLPHIN
ȤФʤ
http://ha3.seikyou.ne.jp/home/okabayashi/toi408qqq.GIF
ǯԥ奦ȡ 71ڡ 0:35:20 HomePage:θ³äƤɤΤ餤23180
ԤԤΡά
125̤Τ褦Ǥ͡ʡ

ɤϤĤְ̤äƤ櫓Ǥο񤷤
̤̪ 71ڡ 0:36:19 MAIL:ishizaki@qa.so-net.ne.jp 23181
Taro
1355C2=125ˤʤΤʡ
71ڡ 0:36:41 MAIL:tarox@nifty.com 23182
ޤ륱
βͤϰʲΣ̤Ȼפޤ

ҤȤĤ礫¾ΣĤ;˶ͤ
¡ҤȤĤ礫¾ΣĤ;˶ͤǸ
ؤϤΣĤΤΤɤ줫ͤ
áɮ񤭤Τ褦

줾βͤĴ٤ȡ
Ϥɤ濴ˤ뤫ǣ̤
¤濴̤ꡢǸ̤ꡢ
Ǹ򣳤ĤΤɤȷ֤ǣ̤ꡢƣ̤
äϣߣߣߣ̤սͤƣdzäƣ̤

̤

ޤΣǤʲͤõƤߤޤ

Ĥǻͳѷ
¡ĤǻѷΤɤ줫Ȥ⤦ҤȤĤ
áĤǻѷĤΣĤ

Ϥɤ֤Ϥˤ뤫ǣ̤
¤ϻѷκ̤ꡢɤ֤ǣ̤ꡢѷ
ɤȷ֤ǣ̤ꡢƣ̤ꡣ
äϻѷлĤĤϷꤹΤǣ̤ꡣ

ס̤
ܤ飴ܤ
ߣߣߣʣߣߣߣˡᣲΣǤơ

ݣᣱ

̤

ȤȤǤĤ롼פˤΤˣ̤
ΤǡΥϣ̤ꡣ

äơΣǤϣܣܣ᣸̤ꡣ

ϣ̤Ǥϡ

71ڡ 0:39:26 MAIL:take4310@mobile.email.ne.jp HomePage:ޤ륱23183
tomh
#23172Τ褦ʹͤ򤷤ɡ
äѤѤʵ
125̤꤬ΤǤ?

ȤǡǧڤǤ褦ˤʤäƤޤ󤫡ޥ뤵?
ԡ 71ڡ 0:39:26 MAIL:tomh@yahoo.co.jp 23184
n
ɤϤĤְ̤äƤ櫓Ǥ
71ڡ 0:39:56 23185

#23183ƱͤǤ
ƽ 71ڡ 0:40:46 HomePage:θ줳ߤ󡪡23187
ԤԤΡά
#23185
ɤϤĤְ̤äƤ櫓Ǥ
䤤䡢ο϶ƤʤΤǤĤְ㤤ޤäƤ뤫餳񤤤Ǥ
̤̪ 71ڡ 0:42:34 MAIL:ishizaki@qa.so-net.ne.jp 23188

äȤϼʼ䤷Ƥ
äѤ᤿
23183Τޤ뤱󤵤β⤦ٹͤ޼
äѤ餤ŷ񡡡 71ڡ 0:44:48 MAIL:hopes@mba.ocn.ne.jp HomePage:ȣϣУţ23189


˸ƽ񤤤ĤǤϤʤǤo

Ϥꤳʣ
71ڡ 0:47:19 23190
ޥ
ɽ򤤤ޤm(__)m
MacOS X 71ڡ 0:49:10 MAIL:masaru-y@kt.rim.or.jp HomePage:23191
ʤ
ˤʤΤǡʥᥤФƿȤǤ
褫ä褫ä

ɤˤⶶܰξ硡ࣲ᣶Ȥ
ܤ礬
ܤȤ
ܤȤ
ˤĤʤȤꡢǡ᣶Ȥ
ܤ礬
ܤΤΤʤΤǡȤ

ǡܣܣᣱȤ
# ѤߡʣȤΰ̣
71ڡ 1:05:15 MAIL:naka@sansu.org HomePage:naka's Home Page23192
tomh
#23183̤
ѥϰʲΤΤǤ͡


60̤






60̤







ԡ 71ڡ 0:55:05 MAIL:tomh@yahoo.co.jp 23193
DrK
Ĥޤ
ƤȤϤʤΤˡ
ξ硢ľƬˤޤǤ60äƤᡣΤʤȹͤƿ褦Ȥνִ֡ʬϡȻפäƤߤȡʬǤ4Ĥζ5Ĥ礬٤뤳Ȥ˵Ťޤ#23183#23192#23193ʤɤ˽񤤤Ƥ̤Ǥ͡
Ƭ⤫᡼#23193Ʊʡ
ϳڱफ?㤦ʡ 71ڡ 1:12:57 MAIL:satoka@star.odn.ne.jp 23194
DrK
#23165ͧοʺ66Фǵޥ뤵34Сκ32ǯ٤ʤΤǡκ11688ȤȤˤʤޤʺα2863ФȤȤʤΤǡ1094
71ߡʺ2410823014ޥ뤵12420ȤȤˤʤޤ
׻褦ˤʤäΤ1983ǯ113衢ɤ˹ԤäƤ⤳ηϪΤǤ
Ƕ;ʤʤäʡǤ̤˲սǯФ뤱ɡ


ϳڱफ?㤦ʡ 71ڡ 1:26:39 MAIL:satoka@star.odn.ne.jp 23195
DrK
#23165ͧοʺ66Фǵޥ뤵34Сκ32ǯ٤ʤΤǡκ11688ȤȤˤʤޤʺα2863ФȤȤʤΤǡ1094
71ߡʺ2410823014ޥ뤵12420ȤȤˤʤޤ
׻褦ˤʤäΤ1983ǯ113衢ɤ˹ԤäƤ⤳ηϪΤǤ
Ƕ;ʤʤäʡǤ̤˲սǯФ뤱ɡ


ϳڱफ?㤦ʡ 71ڡ 1:30:32 MAIL:satoka@star.odn.ne.jp 23196
DrK
#23165ͧοʺ66Фǵޥ뤵34Сκ32ǯ٤ʤΤǡκ11688ȤȤˤʤޤʺα2863ФȤȤʤΤǡ1094
71ߡʺ2410823014ޥ뤵12420ȤȤˤʤޤ
׻褦ˤʤäΤ1983ǯ113衢ɤ˹ԤäƤ⤳ηϪΤǤ
Ƕ;ʤʤäʡǤ̤˲սǯФ뤱ɡ


ϳڱफ?㤦ʡ 71ڡ 1:34:52 MAIL:satoka@star.odn.ne.jp 23197
DrK
졢ƱΤ3񤭹ޤƤ롪
򲡤餳ʤäƤޤޤ
ϳڱफ?㤦ʡ 71ڡ 1:35:54 MAIL:satoka@star.odn.ne.jp 23198
ȥȥ
#23193
ƱǤ
125ǥäΤϤäƽľ⤦ٹͤƤäѤ125
ǼĤŬ5ߤǿޤƤޤ
鲿Ȼ䤬̤Ȥϡ¤1253ܤǤ
ʼ˸лԡ 71ڡ 1:46:45 MAIL:h-sakai@zb3.so-net.ne.jp 23199
BossF
(5C2)C4-{5x(4C2)C4+5C2}
Ρ(5C2)C4䤫4-1ʬ줿Ρ5x{(4C2)C4}3-2ʬ줿Ρ52Ҥޤ
Ǥ⡢δֳ֤ۤɤ⤢ʶ䡢ٻorػʤɤ§ζɤʤ뤫Ǥ
(^^ 71ڡ 4:10:50 MAIL:fv2f-ftk@asahi-net.or.jp HomePage:£ơǣӡԣ£23201

гդѷդ򣴤֤Τ顢ΣǤгդѷ飴
ȡѷξޤ
104-5*64-53=210-75-10=125
äȡܤƣᣴȷ׻ƴְ㤨Ƥޤ
彣λ 71ڡ 5:04:14 MAIL:nikotan@fat.coara.or.jp 23202
ٶ
3ѥζΤͤơǽ85̤ȤѤˤʤäΤǤ
Ǥ褯褯ͤƤߤȡ125̤פȤȤʬޤǤäΤˤؤ餺Խɽ˺ܤʤ塢ԷǼĤˤʤ
īɽߤ60ͤԤ롣⤦ȤפäƤ
顢ʤ19̤˼ʬ̾ܤäƤ롣ޤʴǺԷǼĤ
ޤ
ǤϤ褦ʤ顣
繥ʹ(Ͽ) 71ڡ 6:32:27 MAIL:oirarion@dk.pdx.ne.jp 23203

ľξʣˡĤ˹ԤƤˤʣˡĤ礫飴ĤζФƤʣˤΣѥǤ줾ξοޤ
ʣˡĤ¤顢᣶̤
ʣˡʬ룲ĤʳΣĤ¤飵У᣶̤
ʣˡǷޤΤǡ̤ꡣ
äơܣܣᣱ̤
縩ԤκΤ褯ꡡ 71ڡ 6:54:10 23205
ϥ饮㡼ƥ
Ϥ褦ޤ

Ưޤ
̶彣 71ڡ 7:16:20 HomePage:ϥ饮㡼ƥ湩ؤ˥23206
ޤ륱
Ϥ褦ޤ

ολΰ̲ͤƤߤޤɤ顢ʣݣˤˤʤꤽǤ
ΥȤǤA000272Number of labeled trees on n nodesפȾҲ𤵤Ƥޤ
71ڡ 9:18:57 MAIL:take4310@mobile.email.ne.jp HomePage:ޤ륱23207
kasama
Ϥ褦ޤ
󤵤(#23205)ƱȻפޤ
71ڡ 9:44:35 23208
ISAMU
10C4-5*6C4=135 ʡ
71ڡ 10:02:17 23209
Ҥ
#23193ˤƱǤ
̹Ǥͤ䤹Ǥ

褵Τ褦ʿޤϡؤúǤĤ¤ʪͤȤˤ褯ФƤΤפФޤ
71ڡ 10:15:01 23210
M.Hossie
Фˤ㡣ܤǽ飱̤ȻפäƤޤޤɤϣĤΥȥݥǤ줾첿̤ꤢ뤫׻ޤ

䲽ؤúǤĤ¤ʪ
ͭؤǰֺǽ˰륫 alkane ΰ isomer Ǥ͡Τι¤ȤʨͻʤɤʪȤɤϢͭ뤫ʤɳؽΤǤޤǤ͡
˿ꡡ 71ڡ 12:48:37 23211
Ȥ
1Ȥ⤦餷ˡǤȥǤڤ
ˡǤʤˤ񤯤ȤʤǤƤϤΤΰ㤦
򤤤ϤĤޤ˴طʤǤ
ζ̼ȢȤȤδͤ󤬥ޥ˥ޤDz
οͤȤϡإ顼DzΦФ򤽤ǸΤDVDǸƤޤ
(Ⱦʬ)줫ϤޤȤʤȽ񤱤褦ˤФޤǤϡ
θ˭ԡ 71ڡ 13:11:01 MAIL:nm528@ybb.ne.jp 23212
ɥ󥬥Х
åۥ󡢤ߤʤä󡪤Τ錄ɥ󥬥Х礬ĹˤʤäʤޤĤˣĤζ򤫤Ƥɤˤ⼫ͳˤ褦ˤƺ夲ޤĤޤƤϲ̤Τ뤫ϥΤηäҼڤΤǤޡ֥ϡ֥ϡ֥ϡ
71ڡ 13:13:26 23213
Ĺ
ʤ󤫡פ֤λäΤ褦ʵ
ŷŤˤޤʤäơĤäƸ줽
ۥƥ뤫ΥǤϡ٤ơդΤ԰¤Ǥ
Ƥ󤷤󡡡 71ڡ 13:54:19 HomePage:åȬ23214
uchinyan
ˤϡϾϫޤ󡢤Ǥ͡

ǽ鸫ȤϡñäΤǤƬǹͤƤ뤦˿޷Ȥդ󤬤餬äƤơ
ƻˡοοn=2Ѥ߾夲Ƥߤ褦Ȼפޤ

Ūˡ񤤤ƤޤɽоݤȤʤ륰դͤޤޤդ
(դ; 1ܽФƤο, 2ܽФƤο, 3ܽФƤο, ...)
ǽ񤯤ȤˤޤĤξ(2;2,0,0,0,...)ʤɡ餫˸0¤־ˤϡ
(2;2)Ƚ񤯤Ȥˤޤ
ޤΥդθĿf(2;2)ʤɤȽ񤯤Ȥˤޤޤդf(2)ʤɤȽ񤭤ޤ

ʲĹʤޤƼϤ

* n=2 ξ
(2;2)ǡf(2) = f(2;2) = 1̤ Ǥ

* n=3 ξ
ĤΤĤǤn=2ξŬѤܤ򤽤ˤĤʤ뤳Ȥͤޤ
ƤǤ륰դϡ(3;2,1)Ǥ
(2;2) -> (3;2,1)
Ƚ񤭤ޤΤȤ1ܽФƤĤʤ뤳ȤˤʤΤǡ
1ܽФƤΥդĸꡢ˰2ܽФƤޤ
ε§ϽפǤ
դθĿϡĤ֤Τ3̤ꡢn=2f(2;2)̤ꡢĤʤΤ2̤ꡢǤ夬äդϡ
֡ݡݡפդ2̤νʣ뤳Ȥդޤνʣοϡ1ܽФƤοбޤ
äơ
f(3;2,1) = 3 * f(2;2) * 2 * 1/2 = 3
ʤΤǡ
f(3) = f(3;2,1) = 3̤
Ǥ

* n=4 ξ
Ʊͤˡn=3Υդ1ɲä뤳Ȥͤޤ
1ФƤɲä2̤ꤢäơ1ФƤϰĸѲʤ
2ФƤϰޤ򼡤Τ褦˽񤭤ޤ
(3;2,1) -> (4;2,2) * 2
2ФƤɲä1̤ǡ٤ϡ1ФƤ2ФƤĸꡢ
3ФƤΤǡ
(3;2,1) -> (4;3,0,1) * 1
Ǥ
äơ
f(4;2,2) = 4 * f(3;2,1) * 2 * 1/2 = 12
1/2򤫤Τ˺줺ˡ
f(4;3,0,1) = 4 * f(3;2,1) * 1 * 1/3 = 4
٤ϡf(4;3,0,1)ʤΤǡ1ܽФƤο3ǡ1/3ˤʤޤ
ɡ
f(4) = f(4;2,2) + f(4;3,0,1) = 16̤

* n=5 ξ
Ʊͤ˷׻ޤ
(4;2,2) -> (5;2,3) * 2 or (5;3,1,1) * 2
(4;3,0,1) -> (5;3,1,1) * 3 or (5;4,0,0,1) * 1
(5;3,1,1)ս꤫㤦ŤߤǸ뤳ȤդǤ
äơ
f(5;2,3) = 5 * f(4;2,2) * 2 * 1/2 = 60
f(5;3,1,1) = 5 * (f(4;2,2) * 2 + f(4;3,0,1) * 3) * 1/3 = 60
f(5;4,0,0,1) = 5 * f(4;3,0,1) * 1 * 1/4 = 5
äơ
f(5) = 60 + 60 + 5 = 125̤
줬Ǥ

ޤǤȡդ(5;2,3), (5;3,1,1), (5;4,0,0,1)ʤȤʬΤǡ
Τ褦ʲˡǽǤ

ʤʾη׻ϡ³뤳ȤǽǤ

* n=6 ξ
(5;2,3) -> (6;2,4) * 2 or (6;3,2,1) * 3
(5;3,1,1) -> (6;3,2,1) * 3 or (6;4,0,2) * 1 or (6;4,1,0,1) * 1
(5;4,0,0,1) -> (6;4,1,0,1) * 4 or (6;5,0,0,0,1) * 1
f(6;2,4) = 6 * f(5;2,3) * 2 * 1/2 = 360
f(6;3,2,1) = 6 * (f(5;2,3) * 3 + f(5;3,1,1) * 3) * 1/3 = 720
f(6;4,0,2) = 6 * f(5;3,1,1) * 1 * 1/4 = 90
f(6;4,1,0,1) = 6 * (f(5;3,1,1) * 1 + f(5;4,0,0,1) * 4) * 1/4 = 120
f(6;5,0,0,0,1) = 6 * f(5;4,0,0,1) * 1/5 = 6
f(6) = 360 + 720 + 90 + 120 + 6 = 1296̤

* n=7 ξ
(6;2,4) -> (7;2,5) * 2 or (7;3,3,1) * 4
(6;3,2,1) -> (7;3,3,1) * 3 or (7;4,1,2) * 2 or (7;4,2,0,1) * 1
(6;4,0,2) -> (7;4,1,2) * 4 or (7;5,0,1,1) * 2
(6;4,1,0,1) -> (7;4,2,0,1) * 4 or (7;5,0,1,1) * 1 or (7;5,1,0,0,1) * 1
(6;5,0,0,0,1) -> (7;5,1,0,0,1) * 5 or (7;6,0,0,0,0,1) * 1
f(7;2,5) = 7 * f(6;2,4) * 2 * 1/2 = 2520
f(7;3,3,1) = 7 * (f(6;2,4) * 4 + f(6;3,2,1) * 3) * 1/3 = 8400
f(7;4,1,2) = 7 * (f(6;3,2,1) * 2 + f(6;4,0,2) * 4) * 1/4 = 3150
f(7;4,2,0,1) = 7 * (f(6;3,2,1) * 1 + f(6;4,1,0,1) * 4) * 1/4 = 2100
f(7;5,0,1,1) = 7 * (f(6;4,0,2) * 2 + f(6;4,1,0,1) * 1) * 1/5 = 420
f(7;5,1,0,0,1) = 7 * (f(6;4,1,0,1) * 1 + f(6;5,0,0,0,1) * 5) * 1/5 = 210
f(7;6,0,0,0,0,1) = 7 * f(6;5,0,0,0,1) * 1 * 1/6 = 7
f(7) = 2520 + 8400 + 3150 + 2100 + 420 + 210 + 7 = 16807̤



Ťɤ
f(2) = 1 = 2^0 = 2^(2-2)
f(3) = 3 = 3^1 = 3^(3-2)
f(4) = 16 = 4^2 = 4^(4-2)
f(5) = 125 = 5^3 = 5^(5-2)
f(6) = 1296 = 6^4 = 6^(6-2)
f(7) = 16807 = 7^5 = 7^(7-2)
...

餯̤ˡ
f(n) = n^(n-2)
Ǥ :-)

Ǥ뤫ʤ嵭ˡǤϡä񤷤

P.S.
嵭δطȯƥ˥ޥäΤǤޤ륱󤵤#23207ˤŦޤ
ͭ̾ʤΤǤ͡äȡ
71ڡ 17:18:37 23215

ʤ󤫡˰úǤúǤηλפФ
ġúǤ϶̤ʤäͻҤ㤦ɡ
縩ԤκΤ褯ꡡ 71ڡ 18:52:50 23216
ʤ
轵ͥ顣
־̣夬dzڤ졢Ʒ夬ۤʤΣʿפȤꡣ

#23166 uchinyan 󤬡ʿޤĴ٤Ȥ𤬤ޤ
C dzǧƤߤޤʿޤuchinyan Ʊ̤ޤ
ơʿޤǤäƤϤϤߤĤޤ

֣פǽѤ˻ĤƤߤ¤٤ȤﲼǤϡ
ʿǤ鷺ޤǤ¤٤뤳ȤǤϤޤޤΤФǤ
äȡʿǤ͡

<base 2> 1 0
----- base 2 max 2 -----
<base 4> 1 2 3 0
<base 4> 3 2 1 0
----- base 4 max 4 -----
<base 6> 1 4 3 2 5 0
<base 6> 5 4 3 2 1 0
----- base 6 max 6 -----
<base 8> 3 2 5 4 1 6 7 0
<base 8> 5 2 3 4 7 6 1 0
<base 8> 5 6 7 4 3 2 1 0
----- base 8 max 8 -----
<base 10> 3 8 1 6 5 4 7 2 9 0
----- base 10 max 10 -----
----- base 12 max 8 -----
<base 14> 9 12 3 10 5 4 7 6 11 8 1 2 13 0
----- base 14 max 14 -----
----- base 16 max 12 -----
----- base 18 max 14 -----
----- base 20 max 16 -----
----- base 22 max 18 -----
----- base 24 max 18 -----
----- base 26 max 22 -----
----- base 28 max 22 -----
----- base 30 max 24 -----
----- base 32 max 26 -----
----- base 34 max 29 -----
----- base 36 max 28 -----
----- base 38 max 31 -----
----- base 40 max 31 -----
̳ƻ 71ڡ 20:42:50 MAIL:naka@sansu.org HomePage:naka's Home Page23217
uchinyan
#23215
轵ͥΤ𡢤꤬Ȥޤ
ϤꡢϸĤޤ󤫡
ξȰäơԥ塼Ƿ׻Ǥϡ14ʿĶ򤬤ʤȤˤϤʤ餺
ˤʤΤˤϡŪʾɬפǤ͡
ࡢåǤʤΤʡ
ޤǤȤäơɤȤȤϤʤΤǤ礦
ΰ̲ n^(n-2) Ȥ꤬ĤäƤޤäƤޤ
71ڡ 21:57:00 23218
uchinyan
#23218ؤ
#23215ϡ#23217δְ㤤ǤѤߤޤ
71ڡ 21:59:07 23219
ͧοʺ
ʤޤ628ȤĤδäΤ顢
ĤޤʤƤ򤷤ޤޥͤƱʤơ
γ󤫤饨ĺͭ񤦤ޤȤ
Ϥ줵ˤѡ󤬽񤫤Ƥ褦ʤȤԺξ
ä뤳Ȥޤϼ㤤ǤƬοꤨϤϤ䡢
ɤ褦ʤʤޤޤǤĥޤ
Į 72ʶ 7:16:04 MAIL:tanioka-s@ams.odn.ne.jp 23220

#23220
Ǥͤ
ʤƣǡʤǤ
ǰʬ򤷤Ƥ⣳ФƤʤ
#23218
n^(n-2)ϵǼˡǾǤʤΤǤ礦
ΤϾʤƤɤդФ狼ʤ
縩ԤκΤ褯ꡡ 72ʶ 12:30:55 23221
uchinyan
ˤϡ

(408)ΰ̲ n^(n-2) ξǤ褦ʤΤǡͤޤǤ˾Ҳ𤷤Ƥޤ
ޤĹʤޤƼϤ

ɤȡǤʤȤͤΤäʬˤս⤢Ȼפޤ
ǡŪʾϤˡޤ˻äͤή򼨤ޤ

* ͤηа

󤵤#23221ˤŦΤ褦ˡ̤ͽۤǤƤΤǡŪǼˡȤΤǤ
λˡ(#23215)ǤϡŪʥդηܤƤΤǡn 䤹ȿf(n;...)
ƤäƤޤޤޤ󡣤ǡ¾ˡϺޤ

դħդΤȤơ˽ޤäܿޤ
ǡդΰAꤷФƤܿͤޤn=5 Ǥϡ1ܡ2ܡ3ܡ4ܤξ礬ޤ
ϡAϤǥդ夲ȤˤǤܤƤ뤳Ȥбޤ
(θĿ = ܿ + 1)Ǥϡ롼פϤꤨʤΤǡɡڹ¤ΥդоݤˤƤ뤳Ȥˤʤޤ
(ΤȤϡϾɬפǤ礦롼פϡθĿ = ܿ Ǥ뤳Ȥ餫ʤΤǾάޤ)
äơAꤹȤΤϡڹ¤դκ(롼)ꤷƤ뤳Ȥбޤ
ʬޤˡʤСˤĤʤ륰դθĿϻĤθĿδؿǽ񤱤ޤ
2ܰʾϡĤɤȤĤʤ뤫ǡʬȯޤɬñǤϤʤΤǤ
ƻ˹ͤз׻ǤơnΥդf(n)ȤȡɡΤ褦ʼƳޤ

f(n) = (m=1,n-1) { (n-1)C(m) (p1+p2+...+pm=n-m-1) {(n-m-1)!/p1!p2!...pm! * f(p1 + 1)f(p2 + 1)...f(pm + 1)} }

ǡ(p1+p2+...+pm=n-m-1) ϡ¤ n-m-1 ˤʤ褦0ʾmĤ˴ؤ¤Ȥ뤳Ȥ̣ޤ
ޤf(1)=1 Ȥޤ

μαդf(..)ΰn꾮Τǡդ˵ǼˡβŬѤƷ׻СŪˤϡǽǤ
μϤʤΤǤʣǤΤǡ(¿ʬǤȻפޤ)ޤ׻פĤޤǤ
ǡž򤷤ޤ

׻񤷤ΤϡAФƤξޤ˷׻ǡ줹ˤǤʤ
ȹͤޤʤf(n)2ܤέθg(m,n-m-1)(= g(m,n-1-m))ȤƤޤäơĤޤꡢ

f(n) = (m=1,n-1) { (n-1)C(m) * g(m,n-m-1) }

Ȥơg(p,q)򿷤˹ͤޤ
ΤȤg(p,q)ϡ¾ΤɤȤĤʤƤʤΩޤ॰դƤդɬפޤ
ǽ顢ǤϤʤȻפäΤǤμΰ̣ͤǼǤޤ
ʤμϡAmܽФƤ򤽤ڤ褦ʬ䤷Aޤޤʤ¦ΥդθĿ
g(m,n-m-1)Ȥ뤳Ȥ̣ޤʬ䤫ϡΩиƤ⤪ޤ
ǼϡˤǹԤޤξǸ褦ˡθΩ¸ߤñˤޤ

¹ԤơդθĿؿȤǤ⤤٤Τ⡢ͤƤޤ
Akޤ륰դθĿx^kηȤ褦xδؿf(n,x)ȤޤĤޤꡢ

f(n,x) = (k=1,n-1) (Akܤޤ륰դθĿ) * x^k

ǤʤΤͤƤȤȡ෸η׻ (1+x)^n Ѥ뤳Ȥ褯ޤ
򿿻褦Ȥ櫓Ǥ餫ˡ

f(n) = f(n,1)

Ǥn=2,3,4,5餤ζŪͤǷ׻Ƥߤȡ

f(n,x) = x * (x + (n-1))^(n-2)

ˤʤꤽͽۤĤޤ
ǰʤ餳ľܤ˾ˡϻפĤƤʤΤǤͽۤϡξǰͤˤޤ

* ̲ n^(n-2) Ȥʤ

nͿդդf(n)Ȥޤ
դΰAꤷ˽ޤܿܤޤ
ܿmܤξ硢ڤäơAޤޤʤ¦ΥդθĿͤޤϡ
g(p,q)pĤdzȤĤʤꡢqĤϳȤĤʤäƤʤդθĿȤȡg(m,n-1-m)Ƚ񤱤ޤ
mܤAȤϰۤʤ¦mĤ֤Τ (n-1)C(m) ɬפʤΤǡ

f(n) = (m=1,n-1) (n-1)C(m) * g(m,n-1-m)

ΤȤg(m,n-1-m)ˤϡ¾ȤϤĤʤƤʤΩޤ॰դ줳Ȥդޤ
ˡg(p,q)ˤĤƹͤޤΥռΡpĤqĤʤʬդrĤǤĤʤäƤΤǡ
rĤ֤Τ (q)C(r) ̤ꡢrĤpĤȸΩƤĤʤΤ p^r ̤ꡢʬդθĿg(r,q-r)ġ


g(p,q) = (r=1,q) (q)C(r) * p^r * g(r,q-r)

(pĤ˸ΩȤǡpĤrĤȤĤʤĤʤ˴ñˤʤäƤ뤳Ȥա)
餫ˡg(p,0) = 1 Ǥ(ξ硢pĤθΩˤʤޤ)
f(n)μ٤ȡʬޤ

f(n) = g(1,n-1)

ϡgˤĤƤ򤱤Ф褤ΤǤľܤ˲򤯤ΤϴñǤϤʤǤ
෸νиʤɤդơѤ뤳Ȥͤޤ
(ǡؿ f(n,x) Ƭˤʤ鼡ƳƤޤ)

(p+q)^(q-1) = (r=0,q-1) (q-1)C(r) * p^r * q^(q-1-r)
p * (p+q)^(q-1) = (r=0,q-1) (q-1)C(r) * p^(r+1) * q^(q-1-r) = ... = (r=1,q) (q)C(r) * p^r * r * q^(q-r-1)
(r -> r-1 Ȥ(q-1)C(r-1) = r/q * (q)C(r) ȤäƤޤ)

ʤΤǡ

g(p,q) = p * (p+q)^(q-1)

Ȥʤꡢg(p,0) = 1 Ȥ狼顢˰դ˷ꤷޤ


f(n) = g(1,n-1) = n^(n-2)

Ȥʤޤ

ǡϤǤޤ
ޤΰ̣ꡢ

f(n,x) = g(x,n-1) = x * (x + (n-1))^(n-2)

⤤ޤ
74 15:46:54 23222
uchinyan
#23222ؤ­餫ǤǰΤᡣ

g(p,q)ˤpĤϡդ餹ȡߤˤĤʤ뤳ȤϤǤޤ
ϡ⤷ĤʤäƤ顢pĤϳΥդȤĤʤꡢΥդϷɤAȤĤʤäƤΤǡA̤ƥ롼פǤƤޤǤ
Υդ롼פޤޤʤȤϡˤդȤꡢʬޤ
Ūˤϡ2ǤΥ顼θ(θĿ - ܿ + 롼פθĿ = 1)ȤäƤ⤤θĿεǼˡǤ⤤ˡǤOK
ɡդڹ¤ˤʤ뤳ȤȤäơλޤο(ʿ٥롩)ˤäƤ뤳ȤˤʤäƤޤ
75ʷ 12:15:15 23223
оϩ
ǽϡѷгաʹףˤ飴٤ФʤǤ˾äƺƤߤޤϤͤޤ
ơѷͳѷäƤϹԤʤȵդΤǤġġ
θ塢äƷɡ
Ĥ£ãģŤΤΣ鲿ܶͤ뤫ȾʬƲ򤤤櫓Ǥ
γ 77ʿ 23:17:08 MAIL:pctakada@mail.goo.ne.jp HomePage:Ĥ줭23224