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Search: id:A096815
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| A096815 |
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Triangle, read by rows, such that T(n,k) equals the k-th term of the convolution of the two prior rows indexed by (n-k) and k. |
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+0
2
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| 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 3, 3, 1, 1, 1, 4, 4, 4, 1, 1, 1, 5, 6, 7, 5, 1, 1, 1, 6, 9, 11, 9, 6, 1, 1, 1, 7, 11, 17, 17, 13, 7, 1, 1, 1, 8, 14, 24, 30, 26, 16, 8, 1, 1, 1, 9, 18, 32, 42, 50, 36, 21, 9, 1, 1, 1, 10, 21, 42, 61, 79, 76, 51, 25, 10, 1, 1, 1, 11, 25, 53, 85, 118, 129, 115, 67
(list; table; graph; listen)
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OFFSET
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0,9
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COMMENT
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Row sums are A096816.
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FORMULA
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T(n, k) = Sum_{j=0..min(n-k, k)} T(n-k, j)*T(k, k-j), for n>=k>=1, with T(n, 0)=T(n+1, 1)=T(n, n)=1 for n>=0.
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EXAMPLE
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T(7,4) = 11 = 4-th term of the convolution of row (7-4) and row 4:
T(3,0)*T(4,4) + T(3,1)*T(4,3) + T(3,2)*T(4,2) + T(3,3)*T(4,1).
Rows begin:
[1],
[1,1],
[1,1,1],
[1,1,2,1],
[1,1,3,3,1],
[1,1,4,4,4,1],
[1,1,5,6,7,5,1],
[1,1,6,9,11,9,6,1],
[1,1,7,11,17,17,13,7,1],
[1,1,8,14,24,30,26,16,8,1],
[1,1,9,18,32,42,50,36,21,9,1],
[1,1,10,21,42,61,79,76,51,25,10,1],
[1,1,11,25,53,85,118,129,115,67,31,11,1],...
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PROGRAM
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(PARI) T(n, k)=if(n<k|k<0, 0, if(k<=1|k==n, 1, sum(j=0, k, T(n-k, j)*T(k, k-j))))
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CROSSREFS
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Cf. A096816, A096811.
Sequence in context: A057774 A089355 A136043 this_sequence A124445 A124279 A135225
Adjacent sequences: A096812 A096813 A096814 this_sequence A096816 A096817 A096818
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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 20 2004
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