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A321449型 |
| 按行读取的正三角形,其中T(n,k)是n的两部分数,总共有k个部分。 |
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16
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1, 0, 1, 0, 1, 2, 0, 1, 2, 3, 0, 1, 4, 5, 5, 0, 1, 4, 8, 8, 7, 0, 1, 6, 13, 19, 16, 11, 0, 1, 6, 17, 27, 32, 24, 15, 0, 1, 8, 24, 47, 61, 62, 41, 22, 0, 1, 8, 30, 63, 99, 111, 100, 61, 30, 0, 1, 10, 38, 94, 158, 209, 210, 170, 95, 42, 0, 1, 10, 45, 119, 229, 328, 382, 348, 259, 136, 56
(列表;桌子;图表;参考;听;历史;文本;内部格式)
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偏移
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0,6
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评论
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链接
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配方奶粉
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O.g.f.:乘积{n>=0}1/(1-x^n*(和{0<=k<=n}A008284号(n,k)*t^k))。
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例子
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三角形开始:
1
0 1
0 1 2
0 1 2 3
0 1 4 5 5
0 1 4 8 8 7
0 1 6 13 19 16 11
0 1 6 17 27 32 24 15
0 1 8 24 47 61 62 41 22
0 1 8 30 63 99 111 100 61 30
第六行{0,1,6,13,19,16,11}对以下两个分区进行计数:
(6) (33) (222) (2211) (21111) (111111)
(42) (321) (3111) (1111)(2) (111)(111)
(51) (411) (111)(3) (111)(21) (1111)(11)
(3)(3) (21)(3) (211)(2) (21)(111) (11111)(1)
(4)(2) (22)(2) (21)(21) (211)(11) (11)(11)(11)
(5)(1) (31)(2) (22)(11) (2111)(1) (111)(11)(1)
(3)(21) (221)(1) (11)(11)(2) (1111)(1)(1)
(32)(1) (3)(111) (111)(2)(1) (11)(11)(1)(1)
(4)(11) (31)(11) (11)(2)(11) (111)(1)(1)(1)
(41)(1) (311)(1) (2)(11)(11) (11)(1)(1)(1)(1)
(2) (2)(2)(11)(2)(2)(21)(11)(1)(1)(1)(1)(1)(1)
(3)(2)(1) (2)(11)(2) (211)(1)(1)
(4)(1)(1) (21)(2)(1) (11)(2)(1)(1)
(2)(2)(11) (2)(11)(1)(1)
(22)(1)(1) (21)(1)(1)(1)
(3)(11)(1) (2)(1)(1)(1)(1)
(31)(1)(1)
(2)(2)(1)(1)
(3)(1)(1)(1)
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MAPLE公司
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g: =proc(n,i)选项记忆`如果`(n=0或i=1,x^n,
g(n,i-1)+`if`(i>n,0,展开(g(n-i,i)*x))
结束时间:
b: =proc(n,i)选项记忆`如果`(n=0或i=1,x^n,
b(n,i-1)+`if`(i>n,0,展开(b(n-i,i)*g(i$2)))
结束时间:
T: =n->(p->seq(系数(p,x,i),i=0..度(p))(b(n$2)):
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数学
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表[Length[Join@@Table[Select[Tuples[IntegerPartitions/@ptn],Length[Cjoin@@#]==k&],{ptn,Integer分区[n]}],{n,0,10},{k,0,n}]
(*第二个节目:*)
g[n_,i_]:=g[n,i]=如果[n==0||i==1,x^n,
g[n,i-1]+如果[i>n,0,展开[g[n-i,i]*x]];
b[n_,i_]:=b[n,i]=如果[n==0||i==1,x^n,
b[n,i-1]+如果[i>n,0,展开[b[n-i,i]*g[i,i]]];
T[n_]:=系数列表[b[n,n],x];
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交叉参考
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囊性纤维变性。A000219号,A001970号,A007716号,A008284号,A055884号,A289501型,A317449型,A317532型,A317533型,A320801型,A320808型.
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关键词
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作者
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状态
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经核准的
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