Taro
¤21.522.5ǤΩޤ
621ڡ 0:09:28 30029
sugitakukun
ࡢ̵ޤääƤȤĤǤġʥޥ
ѥ򸫤¤23Τ褦Ǥ35֤ȸäƤޤ褦ʡ

Ȥ21.522.5ΤۤΤ褦ʵƤΤǤϤơ
KKS衡 621ڡ 0:15:35 MAIL:sugitakuunikun@msn.com HomePage:White Shadow30030
ޥ
ޤä...ʤñʥߥ򤷤Ƥޤޤ...ߥƤϸۤɽ񤭤ޤ⸽դΩʤޤ......
PowerBook 621ڡ 0:13:49 MAIL:masaru-y@sansu.org HomePage:30031

ʤΤǤ
621ڡ 0:13:55 30032

36ܤäɬʤ󤸤㡦

⤦äȹͤޤ
621ڡ 0:13:59 30033
ʸ
36ɬ1ˤʤ褦ʡ
621ڡ 0:14:32 MAIL:kyorofumi@msn.com HomePage:ʸ30034
Taro
19.75ΩĤ褦Ǥ̵⡦

(ɵ)18.75,19.25,19.75,20.25,20.75ϤǤ
621ڡ 0:16:57 30035
ߤ
Ū˴㤤ʤΤǽľ

ǽ餬ܤ
ǽ餬ܤ
ǽ餬ܤ

ȤʤäƤޤΤǡܤˣˤϤʤʤϤ
621ڡ 0:22:08 30036
banyanyan
ΥߥǤܤϣΤϤ
Իԡ 621ڡ 0:15:45 MAIL:banyanyanmi@yahoo.co.jp HomePage:뤤²ײݻ30037
tl
ϤοϼȹͤƤǤ͡
621ڡ 0:16:01 30038

Ǹ2110ȤʤΤǡܤϡ1Ǥͤ
ӥå 621ڡ 0:18:19 HomePage:θ30039
35
Ȼפޤ
621ڡ 0:16:40 30040
sugitakukun
#30035
ࡢ̵ˤꤽǤͤ
35ܤ34ܤ1/nȤȡ32ܤ(n1)/nȤˤʤΤʡ

ŬʤȸäƤʤǸڤƤޤ...
KKS衡 621ڡ 0:24:37 MAIL:sugitakuunikun@msn.com HomePage:White Shadow30041
ʸ
ϤοXȤ
X , X-1 , 1 , X-2 , X-3 ,1 ,
3ܿܤ1ˤʤȻפäơ
΢ȻפäǤɡ
621ڡ 0:17:38 MAIL:kyorofumi@msn.com HomePage:ʸ30042
ߤä
Ŭ˲äԤˤʤäΤΡǽˣˤʤͤɤƤ⣳ܤοͤˤʤäƤޤ
դ߼ƤʤߤʤΤǡ⤷Сɤʤ񤤤ĺʤǤ礦
621ڡ 0:18:23 30043

ֹ棰ϤƤޤԤƱߥ
621ڡ 0:18:53 30044
ޥ
ࡢߥޥ...¤ϡʬη׻κݤˡֹֽ棱֤ο֤ͤοͤäơ֤οͤפȤ褦ˤƤäƤޤäƤޤ׻ѻ򸫤顢ΤȤƱȤäƤޤ...

ˤƤ⤦ޤΩʤΤǡʤȤ«ʤͤޤ...
PowerBook 621ڡ 0:18:59 MAIL:masaru-y@sansu.org HomePage:30045

ʤʤ36ܤˣˤʤޤ
621ڡ 0:20:07 30046
banyanyan
餤˺ƥȤȤȤˤƤϤǤ礦
Իԡ 621ڡ 0:20:08 MAIL:banyanyanmi@yahoo.co.jp HomePage:뤤²ײݻ30047
kasama
( )?֢֤ͣʤ(^_^?)
621ڡ 0:20:09 30048

35ͤˤв衩
ӥå 621ڡ 11:58:59 HomePage:θ30049
ե륳
ܤϴ㤤ʤäƤޤޤ
ɤƤ35ܤ036ܤ1ˤʤΤǡ⤷ơĤǧڤ򤫤Ƥߤ顢23Ƥޤޤġ
621ڡ 0:21:50 30050
ޥ
#30047
ߥޥ󡢤ˤ40ʬǿΤϤäȡǽŪˡ̵Ǥ..ʥm(__)m
PowerBook 621ڡ 0:21:57 MAIL:masaru-y@sansu.org HomePage:30051

ֹ棰ϤƤޤԤƱߥ
621ڡ 0:22:25 30052

#30035
16.125ȤǤޤ
621ڡ 0:23:18 30053

䡢ˤƤ⤪äǤ餷ޤ
621ڡ 0:24:08 30054
banyanyan
Ϥ䤹ߤȤȤˤƤϤǤ礦
Իԡ 621ڡ 0:25:03 MAIL:banyanyanmi@yahoo.co.jp HomePage:뤤²ײݻ30055
ޥ
ȡȹͤޤȤꤢ֣֡פäƤȤˤƤޤޤɽϡְΤߡ׷Ǻܤν̤ŤϤʤȤȤˤƤޤ

ߥθϴˡ֥å­פˤޤ#30045˽񤤤褦ʻפߤʤΤǤȿåƤФȯǤȻפޤ٤ޤǵƤäѿޤǤm(__)m
PowerBook 621ڡ 0:25:18 MAIL:masaru-y@sansu.org HomePage:30056

#30056
ʤۤɡ
䤹ߤʤ
621ڡ 0:28:48 30057
banyanyan
/() λ!
Իԡ 621ڡ 0:29:46 MAIL:banyanyanmi@yahoo.co.jp HomePage:뤤²ײݻ30058
sugitakukun
#30035
̵ǤʤǤ͡
36ܤˤʤ34ܤ35ܤAȤ33ܤ2A32ܤA3Aǡġġȵջ򤷤ƤäȤˤɤ3Nܤ1Ȱפ褦ʥѥ󤬲򤫤ʡ

33ܤ2A=1ǡ32ܤA=1/2ΤȤ21.532ܤ3A=3/2ΤȤ22.5ƤʴǤ

ʤޤŬʤΤ¾ˤ⤢뤫⡩

ǤĤ뤫ʤƿʤʤޤʤ

KKS衡 621ڡ 0:33:17 MAIL:sugitakuunikun@msn.com HomePage:White Shadow30059

ǽ21.5ä̾ФʤäΤƤޤ
ǰ¿ӿäƿޤ
轵ϵǰ٤Ǥ͡ӥå꤫ʰ̣

ϺǽοͤδǾʬޤ
褽140٤餤 621ڡ 0:41:27 30060
Melvy
Ф餯 ֽߥ ȼ򤫤ȡͦ 21.5 äͤǤ

#30059
ΤܤΤ 36 ܤޤǤǤʤȤͤͭ¤äݤǤ͡
ʬ 2 ٤Ȼפޤ17+1/6 Ȥˤʤޤ͡
621ڡ 0:42:02 HomePage:رMelvy30061
⡼ޥ
a
a-1
1
a-2
a-3
1
a-4
a-5
1

36ܤ1ǡ
36312
361224
0,1,2,,23

Ǽɤߤޤ ^^
ɤǽ36ܤοͤ0ää褦Ǥ͡
쥤ȥޡǹä^^v

ǽդΥեܥʥåȻפäƤޤǸ夬ɤäƤ⤢鷺ƻ˹ͤ餦ޤޤ^^;v
621ڡ 0:46:49 30062
ʸ
#30059
̵ʤȻפޤ
(2ο)-(1ο)(1ο)-(2ο)
Τɤ餫ʤΤǡ
621ڡ 0:43:25 MAIL:kyorofumi@msn.com HomePage:ʸ30063
Taro
#30059
Ȥꤢ475/322725/256,3231/512ʤʬ줬2߾褬Ǥ
ʬ줬礭ȼ«ˤʤΤDzͭ¤Ǥ褦

Ǥ113/6ʤɤˤʤ뤳Ȥ狼ޤ
621ڡ 0:49:42 30064
Ҥ
ʬ죲ʬ
ʬ죴ʬ

ȡ̵ˤꤽǤ
ʼ˸ 621ڡ 0:50:13 30065
Holly
ȡ¿ʤ 20.6 Ȥˤʤ褦ʵޤ

(ά)1<27>2.61.610.60.40.20.20
621ڡ 0:55:25 30066
ʸ
3k+1ܤˤ
0<A(3k-1)<1ΤȤ
ʹߤ
A(n)=A(n-2)-A(n-1)Ωġ
ʤ鲿̤꤫ϳڤǤ͡
621ڡ 0:53:53 MAIL:kyorofumi@msn.com HomePage:ʸ30068
ʸ
#30064
ʬ6äƤȤϡ
A(n)=A(n-1)-A(n-2)Ϣ³ƽФƤäƤȤǤ͡
621ڡ 0:57:39 MAIL:kyorofumi@msn.com HomePage:ʸ30069
sugitakukun
#30061
3ܤϤ餫1ʤΤǡ̤⤳ޤǤ1ˤʤʤФʤʤΤǤ
Ȥȡ⡹33̤Фޤβǽ٤櫓Ǥ27ܤλǴ10̤ʾ夢ΤǤ衣
#30063Τ褦ˤ줾̤Ϲ⡹2̤ʤΤǤؿؿŪ˲ǽΤǡĤ24ǤäƤȤƤĤʤˤʤ櫓ǡ

եܥʥå3NܤʬˤȤ⡢ǽȤƤ櫓Ǥ

Ƥʤ櫓ǡȤϥץޤ󤢤ˤǤʤ
KKS衡 621ڡ 0:57:41 MAIL:sugitakuunikun@msn.com HomePage:White Shadow30070
ʸ
#30070
Ȥ̤꤫ǤʤǤ͡
621ڡ 1:01:57 MAIL:kyorofumi@msn.com HomePage:ʸ30071
sugitakukun
#30068
ȿ㡧25ܤ13/826ܤ5/827ܤ1ξ硣

13/85/81(27)3/85/82/8(30)3/81/82/8(33)1/81/80(36)

ʤ֤äĤ֤Ƥߤޤ󤬡ʤ櫓ǤιͻϵǤޤ^^;
KKS衡 621ڡ 1:04:05 MAIL:sugitakuunikun@msn.com HomePage:White Shadow30072
Ҥ
ˤƤ⡦
̤ãϡߥޤꤷΤ褦ʲ
ФǤ
ʼ˸ 621ڡ 1:04:59 30073
Taro
#30071
ޡʥѥʤĴ٤Ƥޤ 427/36,463/36,333/28,227/14,241/14,669/46,1057/184,1241/184,2163/446ʤɤȤꤢȽޤʬ줬餤
621ڡ 1:06:07 30074
å
ʥѥ⤢ޤΤǡ
֡49/24or47/24֡25/24or23/24֡24/24
֡1/24֡23/24֡22/24
֡1/24֡21/24֡20/24

34֡1/2435֡1/2436֡0

ʷ⤢ޤ
621ڡ 1:08:06 30075
sugitakukun
#30074
ʬ줬

Ǥ̤͡ιͤ3NܤɬAζܤˤʤ櫓ǡʤĤܢʹܢͶܤη֤ˡ줬1ˤʤȹͤʬɬˤʤϡĤ
KKS衡 621ڡ 1:13:35 MAIL:sugitakuunikun@msn.com HomePage:White Shadow30076
Melvy
Ϥʬ饹ȤȤȡ(ʹʬѤʤȤ)
ɬʬҤ 1 () ΤǡʬҤդɤ
ƱήѤäƤȤˤʤޤ͡
θĿĴ٤Τ˻ȤΤǤϤʤʡȻפäƽ񤭹ߡ
ʤʬˤȤϤοʬ줬Ǥ뤳Ȥϴְ㤤ʤǤ ()

() #30059 εˡǡοʬҤϤ٤ A ʬҤܿ
äơ⤷ A ʬҤ 1 ǤʤʤС­ 1 ˤʤ 2 Ĥο
ФƤΤϤοʬǤ뤳Ȥȿ롥

() ʬ줬ȡ
(ά) 1 (3N ) ʬҤ ( or ) ʬҤ ( or ) ʬҤ (3(N+1) )
ȤʤäơФ 3 ܿܤ 0 ʤ
621ڡ 1:19:50 HomePage:رMelvy30077
㡼ߡ
35 ʬ̤ n ѤȤθĿϥեܥʥåˤʤ롩
褦ʵޤ
𡡡 621ڡ 1:21:58 MAIL:ojamaru@amber.plala.or.jp 30078
ʸ
A(n-2),A(n-1)Ȥ1ΤȤ
ɬA(n-2)>A(n-1)ʤΤA(n)=A(n-2)+A(n-1)
Ǥ뤫
ϤA(n-2)<1ȤʤäȤ
A(n)=A(n-1)-A(n-2)
Ȥʤ

A(3k+1)ǽ1̤ˤʤäȤ
n=3k+1ʹߤ
A(n)=A(n-1)-A(n-2) A(n)=A(n-2)-A(n-1)2̤ͤΤ
2^(34-3k)̤¸ߤ롩ͽۡ

A(3k+2)ǤϤ1̤ˤʤäȤ

狼ʤ

ʤ󤫽ʣȤ¸ߤʤΤäꤷǤ͡
621ڡ 1:24:54 MAIL:kyorofumi@msn.com HomePage:ʸ30079
ǥ
ΤʤˤɤɤͻʤǤޤ͡ߥ⻻ذ
ˤȤäƤϿʳڤѤäƤޤȤ򤤤Ǥ͡

Ȥǡ35֡פƤּפȤȤʤȡ֡ݣפ
ˤʤޤ͡
621ڡ 2:07:44 30080
ʸ
A(3k+2)ǤϤ1̤ˤʤäȤäƤΤ
ǽο
A(3k+1)ǽ1̤ˤʤäȤο1Τˤʤ󤸤ʤͽۤƤߤ롦
֤󤢤X򸫤Ĥ顢֤X+1ޤX-1Τɤ餫դȻפޤ

ƤȤ
11
22^(34-3k)̤
k=1
ʤͽۤơޤ
䤹ߤʤ
621ڡ 1:45:04 MAIL:kyorofumi@msn.com HomePage:ʸ30081
㡼ߡ
0 - 1 - 1 - 2 - ȵդˤɤäƤȤͤ롣
a(1), a(2), a(3), a(4) Ȥ롣
a(1) a(4) Τ褦ᡤ
a(n+2) = a(n+1) a(n) Ƥ
(ʣ - a(n+1) > a(n) ξΤ)
m ܤޤ줿դ鸫ȡ
ǽ ֺ 1 ʳξ򤹤٤Ƥ롣

m ܤǽ 0 Ȥʤ롤դ ȡ
־嵭οΤ a(m) > a(m-1) Τγƹ
1/(a(m) - a(m-1)) ܤƵդ鸫Ρ 1 1 б롣
[ϤȾۤΤɾά]

m ܤޤǤοΤm ܤ + 줿Τ
p(m) (ΤȤ a(m) > a(m-1) : 줬θĿб)
- 줿Τ q(m) (ΤȤ a(m) < a(m-1)) Ȥ롣
p(m+1) = p(m) + q(m)
(a(m) ޤޤäƤмưŪ a(m) + a(m-1) OK)
q(m+1) = p(m) ( a(m) > a(m-1) Ǥʤޤʤ)
ΩΤǡ (Ƚ) Ѥ
θĿɽ p(m) եܥʥåǤ뤳Ȥ롣

ޤ˴ñˤäΤǡɤְ㤨Ƥ뤫⤷ޤ
𡡡 621ڡ 2:05:10 MAIL:ojamaru@amber.plala.or.jp 30082
BossF
ǽäƤʤäΤʡ(=^^=)
Tokio 621ڡ 4:36:47 MAIL:fv2f-ftk@asahi-net.or.jp HomePage:BossF's Toy Box30083

#30080
ξ郎ʤȡ-19,23ǤOKǤ͡
ԡ 621ڡ 7:40:42 30084
ϥ饮㡼ƥ
Ϥ褦ޤ

פǤͤν񤭹ߤƤޤ
621ڡ 8:57:38 HomePage:湩ؤ˥30085
uchinyan
ϤϤ褦ޤơϡ
Ѥä褦Ǥ͡ǤäǼĤɤߤޤ
λβˡϤʤꤤøǡǽοȤȡʤΤǤ§Ƨޤơ
ݣݣݣݣݣݣݣݣݣݡݡݣܡ
ʤΤǡʤȤȤǧڤޤ (^^;
ͥνȡ 621ڡ 9:14:35 MAIL:uchi@sco.bekkoame.ne.jp 30086
uchinyan
ǼĤɤߤޤ

ǽʸ褯ʬʤΤǡ޳ѤεǤ¿ξιͻä˲θĿȤϡ褯ʬޤǤ

(äɲ)
Ѥߤޤ󡣰ʲϡξǤ͡
(ɲý)
ʤǤ⡤ǽοοʤʤȻפޤ
ʤС#30086ˤơ
ݣϣǤʤΤοǡ缡ݢϣܤޤǤϾäƣʾ塤ȤʤäƤ
ɡ#30086ˡǤ
Ǥ⤤Ȥʤȡݣ㣰ǡϺʤΤǣܤޤǤοǡ
ݣݡݡݡݡݣݡݣݡݣݡݣݡݣݡݡݣܡ
ݣ⤢Τ褦Ǥ͡
ͥνȡ 621ڡ 13:29:47 MAIL:uchi@sco.bekkoame.ne.jp 30087
եܥʥå
ǼǤ줫򸫤ҤȤΤˡ֤ϼפȤǤ͡
621ڡ 12:33:36 30088
ޥ
ȡʸǤ֣͡פ֣͡פȤʤäƤޤm(__)m

#30088,#30084,#30080
Ŧ꤬Ȥޤ֣礭פȤɽˤƤޤʤʤȤʤֻפο¸ߤϹͤʤƤ...ȤˤĤʤäƤޤäơ˺ƤޤǤ...
PowerBook 621ڡ 13:05:38 MAIL:masaru-y@sansu.org HomePage:30089
uchinyan
#30028
⡼ޥ󤵤ء
#30027ϡľŪˤ餫Ȼפְ㤤ǤϤʤǤȤ̣ǤϻǤ
̩ˤϡŪǼˡȤФȻפޤ(9 νиλεǼˡǤ⡤񤭲ΤϷ빽ݤ)

ͧͤβˡϡʤۤɡäȤޤäƤ褦Ǥ쥹ߥ褦Ǥ
βǤ

f(n) = n + S(n) Ȥn οʣΰ̤οˤ 9ǤʤС f(n+1) = f(n) + 2 Ǥꡢn ο9ʤСf(n+1) < f(n) Ǥ롣
ϡεƱǤ줫ɡf(n+1) <= f(n) + 2 Ǥ

f(1) = 2 ǡf(n) > n 顢Ǥդ2ʾμ m ֤Ȥf(n) m μ n ¸ߤ롣
n < n + S(n) = f(n) ʤΤǡn f(n) ñĴäǤϤʤˤƤäޤ
ǡ2 ʾμ m СĤϡf(n) m Ķޤ
f(n) ñĴäǤϤʤΤǡm ĶäβǽϤޤn < f(n) ʤΤǡ
ʤȤ m <= n ȤʤСμ¤ˡm < f(n) Ǥ
äơɤǡf(n) <= m ˤʤʤꡤΰǤ f(n) <= m Ȥʤ n ¸ߤ
n+1 ФƤ m < f(n+1) ȤʤϤǤ줬f(n) <= m Ȥʤ n ΰ̣Ȼפޤ

m < f(n+1) ǡf(n+1) f(n) + 2 顢f(n) m ʤСf(n) = m+1 Ȥʤ롣
n+1 Ǥ m ĶΤ m < f(n+1) Ǥ줫顤m < f(n+1) <= f(n) + 2 <= m + 2 Ǥ
Ǹϡf(n) = m Ȥʤ n äǤ
m Ϳ f(n) Ȥʤ n С n ȤäƤФǤ
f(n) not= m ξϡۤɤμϡ
m < f(n+1) <= f(n) + 2 < m + 2
Ǹˤ椬դޤ󡣤Ȥʤȡf(n+1) ϼ m m+2 δ֤ˤΤǡf(n+1) = m+1 Ǥ
Ĥޤꡤm ٤μ m+1 Фդ n+1 ¸ߤ뤳Ȥ򼨤Ƥޤ
ǡ٤礦ξʤȤ n + S(n) Ȥ뤳Ȥʬޤ
ʤͧͤκǸΡf(n) = m+1פϡf(n+1) = m+1 ΥߥȻפޤ
ͥνȡ 621ڡ 13:47:10 MAIL:uchi@sco.bekkoame.ne.jp 30090

23/1,59/3,61/3,89/5,91/5,97/5,1/19,75/19,77/19,41/21,43/21,17/35,
33/35,19/37,35/37,41/39,59/39,97/39,43/41,61/41,3/49,33/49,3/53,
35/53,73/55,79/59,15/61,57/61,47/63,59/63,49/65,61/65,17/67,63/67,
73/69,5/71,57/71,75/71,89/71,5/73,29/73,77/73,91/73,79/75,5/77,31/77,
5/79,13/79,63/79,73/79,97/81,69/83,77/83,7/85,29/85,41/85,71/85,
73/85,79/85,11/89,15/89,29/89,43/89,81/89,83/89,9/91,31/91,47/91,
81/91,97/91,31/95,49/95,83/95,87/95,7/97,83/97,85/97,89/97,89/99

˸¤ʤС˹礦ʬʬ100ޤǤǤäѤޤ
621ڡ 15:26:26 30091
uchinyan
#30082
㡼ߡ
ʤۤɡäȤäꤿȤʬޤ (^^;
(äɲ)
#30091Τ󤵤β򸫤ƤƻפäΤǤ
㡼ߡˡϡܤοͤομ¿ξͤƤ褦Ǥ
ʸˤȡܤοͤοϡ֤ϤοݣפǤäơǤϤʤΤǡ
Ϥο¿ξˤϡܤοͤοǤ褵Ǥ
(ϤοʤСϤꤨʤ)
ʲεϡܤοͤο⺹ȤơĤޤοȤưäƤ褦ǡ
ϰϤǤǤܤοͤομ¿ξȴƤ褦˻פޤ
ϤοξȴƤʵޤ
ɡεϡ٤ƤοξͤƤ褦Ǥ
(ɲý)

0 - 1 - 1 - 2 - ȵդˤɤäƤȤͤ롣
a(1), a(2), a(3), a(4) Ȥ롣
a(1) a(4) Τ褦ᡤ
ޤǤOK
a(n+2) = a(n+1) a(n) Ƥ
(ʣ - a(n+1) > a(n) ξΤ)
ʣ - Τ a(n+1) > a(n) ξΤߤǤɬΤǤϤʤa(n+1) > a(n) ǤäƤ + äƤǤ͡
ޤʤСʾ礬ФƤʤΤǡäĤʤޤ͡
򤫤ʤȤˡޤϡǤĤޤŤ (^^;
䤳 m ܤޤ줿դ鸫ȡ
ǽ ֺ 1 ʳξ򤹤٤Ƥ롣
OK

m ܤǽ 0 Ȥʤ롤դ ȡ
ϡ鸫Ρm ܡס
־嵭οΤ a(m) > a(m-1) Τγƹ
1/(a(m) - a(m-1)) ܤƵդ鸫Ρ
äϡǽ餫鸫Ρm ܤ (m-1) ܡסʤ꺮𤷤ޤ (^^;
1 1 б롣
[ϤȾۤΤɾά]
a(n) κ餷ơʤ餫äݤޤ¿ʬפǤ礦

m ܤޤǤοΤm ܤ + 줿Τ
ϡǽ餫鸫ơm ܡס
p(m) (ΤȤ a(m) > a(m-1) : 줬θĿб)
ϤϡۤɤбOK
- 줿Τ q(m) (ΤȤ a(m) < a(m-1)) Ȥ롣
OK
p(m+1) = p(m) + q(m)
(a(m) ޤޤäƤмưŪ a(m) + a(m-1) OK)
⡤餫Ǥ礦+ ϤĤǤޤ顣
q(m+1) = p(m) ( a(m) > a(m-1) Ǥʤޤʤ)
OKåξ郎ɬפǤ顤m ξ p(m) ̣ޤ
䤬ΩΤǡ (Ƚ) Ѥ
ֽ͡פȤΤϡp(m) ν͡m >= 4 ǰ̣Τǡp(4) = 1, p(5) = 1 ʡ
θĿɽ p(m) եܥʥåǤ뤳Ȥ롣
ϤΤ ^^/

䤢ޤ˴ñˤäΤǡɤְ㤨Ƥ뤫⤷ޤ
꤬ȤбդǤ礦פȻפޤ

Ǥ⥹ꥢ륿Ǥޤǵդʤơ
ϰͤƤʬʤʤ(©)
ͥνȡ 621ڡ 18:27:41 MAIL:uchi@sco.bekkoame.ne.jp 30092
⡼ޥ
#30090
uchinyanء
ʤۤɡʬ䤹꤬ȤޤOrz
錄ˤ񤷤Ǥ^^;
ޤꤤޤäv
621ڡ 17:08:46 30093

ǽΣĤǤǤ⤪餯եܥʥåˤʤꤽǤ
θĿP(n)ϡnܤΥեܥʥå F(n)Ȥȡ
P(1)=1,P(2)=1,P(3)=0
P(n)=F(n-3)4n7
P(n)=F(n-3)+F(n-6)
=2*F(n-4)7n
ˤʤΤʡ
ͽۤäƤС2*2,178,309=4,356,618̤ꡩ
ʪɤ߾ 621ڡ 17:27:22 30094
㡼ߡ
(0 ʳ) ξͤޤ
Ƥ⤪餯٤ǤǤ礦
(ȡ˹ͤ˴ФǸäƤߤ)
ä̲Ȥ˽񤤤ΤˤʬäȻפޤ
ʤȤä褦ǰ¿ޤ ()
𡡡 621ڡ 20:19:23 MAIL:ojamaru@amber.plala.or.jp 30095
uchinyan
#30094
tkء
ϤɤΤ褦˹ͤ줿ΤǤĺȤ줷ΤǤ (^^;
ȡͽۡפȤΤϡñ˱θʤäƤΤʡ
ͥνȡ 622ʶ 8:52:04 MAIL:uchi@sco.bekkoame.ne.jp 30096

#30096
P(n)n412餤ޤǤ׻͡ʸˤɤäƹԤޤˤͽۤƤƤߤǤ
ͽۤȤΤϡ㡼ߡߤ˾ΤϤäդǤʤΤǡ

ޤλʬʺǽΣȺǸΣȴΤλʬˤθĿp(n-1)ˤʤäƤ褦ʤΤǡ2ܤθθĿǤ
nʬ礭Ȥʤξ6nˡθθĿθĿǤ
n=4,5ΤȤ줾Ų⤷դˤƤϤޤʤˤʤߤǤ

٤ϡޤλʬΤθĿp(n-1)ˤʤäƤ뤳Ȥȡ
ǽΣĤξʤȤˤʤäƤθĿեܥʥåˤʤäƤ뤳
ȻפޤԤp(n)餫ʡ
ԤԤäƤСեܥʥåäƤ뤫ȡ
ʪɤ߾ 622ʶ 18:21:41 30097
uchinyan
#30097
tk󡤤꤬ȤޤʤۤɡͽۤäΤǤ͡

⡤Ū n = 12 餤ޤĴ٤ƤߤơΤʡȤϻפޤ
㡼ߡμˡβɤ򾯤ͤƤߤơp(m) 񤭴Ф褵ʴƤΤǤ
ޤǤƤʤΤѤʼˤʤäƤޤäƹԤͤäƤޤޤ (^^;㡼ߡ󡤥إס

ʤ褯ǤƤʤΤǴ㤤ƤȻפޤ

ޤλʬΤθĿp(n-1)ˤʤäƤ뤳Ȥ
ϰդ˷ޤ뤷ǽ 1 ȤΤޤäƤΤǡΤˤʵ⤷ޤ͡

ǽΣĤξʤȤˤʤäƤθĿեܥʥåˤʤäƤ뤳
äϤɤʤΤǤ礦ǽդεưˤʤޤ
P(n) ޤλʬθĿޤʤСطʤΤʡ
ͥνȡ 622ʶ 23:29:27 MAIL:uchi@sco.bekkoame.ne.jp 30098
㡼ߡ
> p(m) 񤭴Ф褵ʴ
֤󤽤ǤǤȻפޤ衣֤ääƤߤޤ͡
𡡡 623ڡ 0:41:13 MAIL:ojamaru@amber.plala.or.jp 30099
粬ҹ
פ֤ޤʡ
ȶȤǿͿѤäƤΤǴͤޤ
οͿ
ʡܣ
ʡܣ
ʡܣˡοˡʡˤο­ȿͿˤʤ롣Ȥ䤳Ǥʡ
äơ衹ϷޤΤǺϲȤʡ

СӡᤤΤǤäȤ֤˴ޤޥ뤵ʡˣ֡

623ڡ 11:39:53 30100
uchinyan
#30099
㡼ߡtk󡣰
ݤʤΤǾȴǽ񤭤ޤ䤬㡼ߡμˡľƤϡѷǽ
p(m) = 2 * p(m-1) - p(m-3), p(6) = 2, p(7) = 4, p(8) = 6
Ǥ򤯤ȡp(8) = p(7) + p(6) Ƥ뤳Ȥ顤եܥʥåΣܤˤʤ뤳Ȥϼޤ
äơtk#30094ͽۤΤȻפޤ

ʳ˼ľפ¿ʬפȤϻפΤǤ
ƳΤפʥޥʥäΤ q(m) ȤΤǤ
μ§ΤǤݤǡäȴñ˥åǤʤ
äľܤ˥եܥʥåʤ
ʤɤĤäƤޤ
ͥνȡ 623ڡ 23:56:32 MAIL:uchi@sco.bekkoame.ne.jp 30101

35ܤޤ0ǤʤΤǡοȤȡ
𡢣ݣݣݣȤˤʤޤ
35ܤϣ-23ʤΤǣ23Ȥʤޤ
äƤϤɤǤ
625ʷ 21:19:55 30102
doba
ߤޤ椫ɤ߻Ϥ᤿顢ɤˤĤƵƤΤ
狼ʤäΤǡ¿ʬȤȤȤǡƤߤޤ


Ѥ
a(1)=
a(2)=-1
a(k)=|a(k-2)-a(k-1)|k=3,4,,n
ͭ¿{a(k)}k=1,2,,nˤ
a(k)0k=1,2,,n-1
a(n)=0
Ȥ
Τ褦ʦθĿ衣
n6Ȥ롣


ˡ
ͭ¿{b(k)}k=1,2,,nˤ
b(k)=a(n+1-k)/a(n-1)
ȡͭ¿{b(k)}k=1,2,,nˤ

b(1)=0
b(2)=1
b(k)=|b(k+2)-b(k+1)|k=1,2,,n-2
b(k)0k=2,3,,n
b(n)b(n-1)


ξķޤС
ͭ¿{b(k)}k=1,2,,nˤϰդޤ롣

ޤﷲؤͭ¿{b(k)}k=1,2,,nˤķޤС
=b(n)/(b(n)-b(n-1))
a(k)=b(n+1-k)/(b(n)-b(n-1))k=1,2,,n
ȤȤˤꡢ
ͭ¿{a(k)}k=1,2,,nˤξȤˤʤ롣
ʤΤ褦ͭ¿{b(k)}k=1,2,,nˤƳ
ξɬ¸ߤ롣

ʾꡢξ
ﷲؤͭ¿{b(k)}k=1,2,,nˤ
Уб롣
äơθĿ뤳Ȥϡ
ﷲؤͭ¿{b(k)}k=1,2,,nˤθĿ뤳Ȥ
ƱǤ롣
626ʲС 0:33:45 30103
doba
ʲθƤ˽Ǥ


b(1)=0
b(2)=1
b(k)=|b(k+2)-b(k+1)|k=1,2,,n-2
b(k)0k=2,3,,n
b(n)b(n-1)
褦ͭ¿{b(k)}k=1,2,,nˤθĿ衣
n6Ȥ롣


b(1)=|b(3)-b(2)|
b(3)=1Ǥ롣
ޤ
b(k)=|b(k+2)-b(k+1)|Ǥꡢʤġb(k)0Ǥ뤳Ȥ
b(k+2)=b(k+1)+b(k)ޤb(k+2)=b(k+1)-b(k)Ǥꡢ
ʤġb(k)0Ǥ뤳ȤƱͤǤ롣

äơͿ줿{b(k)}٤ϡ
b(1)=0
b(2)=1
b(3)=1
b(k+2)=b(k+1)+b(k)ޤb(k+2)=b(k+1)-b(k)k=2,3,,n-2
b(k)0k=2,3,,n-2
b(n-1)0b(n)0
b(n)b(n-1)
ȸ롣

ޡ1mn-5ǤmˤĤơ
c(1)=0
c(2)=1
c(3)=1
c(k+2)=c(k+1)+c(k)ޤc(k+2)=c(k+1)-c(k)k=2,3,,m+1
c(k)0k=2,3,,m+3
褦ͭ¿{c(k)}k=1,2,,m+3ˤͤ
N(m)
Τc(m+3)=c(m+2)+c(m+1)ǤΤθĿP(m)
c(m+3)=c(m+2)-c(m+1)ǤΤθĿQ(m)Ȥ롣

m=1ΤȤ
c(4)=c(3)+c(2)ޤc(4)=c(3)-c(2)Ǥ뤬
c(2)=c(3)=1,c(4)0ʤΤǡ
ɬc(4)=c(3)+c(2)Ȥʤ
äơP(1)=1Q(1)=0

2mn-5ΤȤ
⤷c(m+2)=c(m+1)+c(m)ʤС
c(m+2)c(m+1)0ʤΤǡ
c(m+3)=c(m+2)+c(m+1)ǤäƤ
c(m+3)=c(m+2)-c(m+1)ǤäƤ
c(m+3)0Τǹʤ
⤷c(m+2)=c(m+1)-c(m)ʤС
c(m+1)c(m+2)0ʤΤǡ
c(m+3)=c(m+2)+c(m+1)ξc(m+3)0
c(m+3)=c(m+2)-c(m+1)ξc(m+3)0Ȥʤȿ롣
äơ
P(m)=P(m-1)+Q(m-1)
Q(m)=P(m-1)

PΤߤˤĤƤȡ
P(1)=1,P(2)=1
P(m)=P(m-1)+P(m-2)2mn-5
äơP(m)ϥեܥʥåmF(m)

Q(m)=P(m-1)=F(m-1)2mn-5
N(m)=P(m)+Q(m)=F(m)+F(m-1)=F(m+1)2mn-5
N(1)=P(1)+Q(1)=1=F(2)

m=n-5ΤȤͭ¿{c(k)}k=1,2,,m+3ˤ
ͭ¿{b(k)}k=1,2,,nˤƬn-2ǤΤǡ
{b(k)}ΤΥХꥨοN(n-5)=F(n-4)

b(n-1)b(n)٤ϡ
b(n-1)0b(n)0
b(n)b(n-1)
Ǥ롣
ǡb(n-2)0b(n-3)0b(n-2)b(n-3)Τǡ
b(n-1)=b(n-2)+b(n-3)ǤäƤ⡢b(n-1)=b(n-2)-b(n-3)ǤäƤ
b(n-1)0Ω롣
ޤb(n-2)0ꡢ
b(n)=b(n-1)+b(n-2)ʤb(n)b(n-1)Ω뤬
b(n)=b(n-1)-b(n-2)ʤb(n)b(n-1)Ȥʤꡢȿ롣
äơb(n)0ξ̵뤹С
ǽ{b(k)}ο2F(n-4)Ȥʤ롣
Ȥϡb(n)=0ȤʤФ褤

b(n)=0ȤʤˤĤƹͤȡ
b(n-1)b(n)=0ʤΤǡ
b(n-1)=-xȤȡ
b(n-2)=x
b(n-3)=2x
b(n-4)=x
b(n-5)=x
b(n-6)=0
ȤʤΤǡ
n=7ǡ{b(k)}=0,1,1,2,1,-1,0ξǤ뤳Ȥ狼롣

ʾꡢĿ
n=6ޤn8ΤȤ2F(n-4)
n=7ΤȤ2F(n-4)-1=3
Ȥʤ롣



n=7ΤȤϡ㳰äơĤǤϤʤĤǤ͡
n=5ʲϼ̤
n=2
n=3
n=4
n=5

ˤƤ⡢սˤɤäʬȤȯۤϤФ餷Ǥ͡
626ʲС 1:49:00 30104
uchinyan
doba󡤹ͻ꤬Ȥޤ

#30103
ϤȤǤ

#30104
Ϥϡʤפ鷺ʬζ򤫤ø˾ФäƤޤޤ (^^;
㡼ߡ#30082Ϥ餺ˡn-1, n ̰Ǥ褫ä
n-1 ΤȤϡξǽǡߣn ΤȤϡܤʤΤǡߣȤ櫓ǡ㡼ߡη̤顤եܥʥåߣȤ櫓Ǥ͡

#30101ϡ㡼ߡp(m)dobaP(m)or N(m)ˤʡ n-2 ǤϤʤ n 夲ͤΤǡ
n-2 ιबȤʤΤĤɬפꡤʤݤˤʤޤ
#30101Τ褦ʥ쥤ʼˤޤȤޤƱ̤ˤʤäΤǤ(ƳФϴְäƤ뤫⤷ʤ)
äơ p(m) ϳΤȤϰۤʤꡤǽ餫եܥʥåΣܤˤʤäƤޤ
ʤΤˡp(7) 㳰 3 ǤǤ⡤p(8) ͤͿ̵ʤ褦Ǥ
(٤ΤǾʤޤºݤɬפʤΤ q(7) = 4 Ǥ
μǤϰ̤ p(m) = q(m) ʤΤǡŤδְ㤤껦ơp(7) = 4 ȤƤޤäƤޤä褦Ǥ)
ͥνȡ 626ʲС 12:44:08 MAIL:uchi@sco.bekkoame.ne.jp 30105
ޥ
http://www.shuwasystem.co.jp/cgi-bin/detail.cgi?isbn=978-4-7980-1700-6

ɤ褦䤯ФߤǤ򤪴ꤤˤϡץ뤬Ϥޤ餹ˤꤤޤʻޤʪäƤʤΤ...

# ɽǥ֤ʤ...orz

PowerBook 626ʲС 12:40:54 MAIL:masaru-y@sansu.org HomePage:30106
uchinyan
#30106
褤Ǥڤ ^^
ͥνȡ 626ʲС 12:49:40 MAIL:uchi@sco.bekkoame.ne.jp 30107
tl
#30106
ɽϤƤоɼԡ 鿴ԡϡ
626ʲС 14:08:29 30108

Τˡ2ब0ˤʤ㳰С1ब0ˤʤ㳰⤢Τ
ȤȤϡθĿˤʤʤ㳰n=4,5,7Σġʤn3Ͻ
ɡ#30094ͽۤϴְäƤΤġ
ʪɤ߾ 627ʿ 0:04:30 30109