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Search: id:A131909
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| A131909 |
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Triangle, read by rows, where T(n,k) = T(n-1,k-2) + T(n-1,k-1) for n>=k>1, with T(0,0)=1 and T(n,0) = T(n+1,1) = T(n-1,n-1) for n>0. |
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+0
2
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| 1, 1, 1, 1, 1, 2, 2, 1, 2, 3, 3, 2, 3, 3, 5, 5, 3, 5, 5, 6, 8, 8, 5, 8, 8, 10, 11, 14, 14, 8, 13, 13, 16, 18, 21, 25, 25, 14, 22, 21, 26, 29, 34, 39, 46, 46, 25, 39, 36, 43, 47, 55, 63, 73, 85, 85, 46, 71, 64, 75, 79, 90, 102, 118, 136, 158, 158, 85, 131, 117, 135, 139, 154, 169
(list; table; graph; listen)
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OFFSET
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0,6
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COMMENT
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A119262(n) is the number of B-trees of order infinity with n leaves.
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FORMULA
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Row sums equal powers of 2. T(n,0) = A119262(n+1) for n>=0, where g.f. G(x) of A119262 satisfies: G(x) = x + G(x^2/(1-x)).
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EXAMPLE
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Triangle begins:
1;
1, 1;
1, 1, 2;
2, 1, 2, 3;
3, 2, 3, 3, 5;
5, 3, 5, 5, 6, 8;
8, 5, 8, 8, 10, 11, 14;
14, 8, 13, 13, 16, 18, 21, 25;
25, 14, 22, 21, 26, 29, 34, 39, 46;
46, 25, 39, 36, 43, 47, 55, 63, 73, 85;
85, 46, 71, 64, 75, 79, 90, 102, 118, 136, 158;
158, 85, 131, 117, 135, 139, 154, 169, 192, 220, 254, 294; ...
Illuistrate T(n,k) = T(n-1,k-2) + T(n-1,k-1):
T(5,3) = T(4,1) + T(4,2) = 2 + 3 = 5;
T(6,4) = T(5,2) + T(5,3) = 5 + 5 = 10;
T(8,3) = T(7,1) + T(7,2) = 8 +13 = 21.
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PROGRAM
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(PARI) {T(n, k)=if(k<0|n<k, 0, if(n==0&k==0, 1, if(k==0, T(n-1, n-1), T(n-1, k-2)+T(n-1, k-1))))}
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CROSSREFS
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Cf. A119262 (columns 0, 1, and main diagonal); A131910 (central terms).
Sequence in context: A043276 A064742 A106638 this_sequence A131730 A029335 A029257
Adjacent sequences: A131906 A131907 A131908 this_sequence A131910 A131911 A131912
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KEYWORD
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nonn,tabl
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), Jul 26 2007
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