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Search: id:A132289
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| A132289 |
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Triangle, read by rows of 2n+1 terms, where T(n,k) = T(n,k-1) + T(n-1,k-1) for 2n>=k>0, T(n,2n-1) = T(n,2n-2) + T(n-1,n-1) and T(n,2n) = T(n,2n-1) + T(n-1,n-1) for n>0, with T(n,0) = T(n-1,n-1) for n>0 and T(0,0) = 1. |
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+0
2
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| 1, 1, 2, 3, 3, 4, 6, 9, 12, 12, 15, 19, 25, 34, 46, 58, 58, 70, 85, 104, 129, 163, 209, 267, 325, 325, 383, 453, 538, 642, 771, 934, 1143, 1410, 1735, 2060, 2060, 2385, 2768, 3221, 3759, 4401, 5172, 6106, 7249, 8659, 10394, 12454, 14514, 14514, 16574, 18959
(list; table; graph; listen)
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OFFSET
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0,3
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COMMENT
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Column 0 and the right-most border (shifted right) equals A125276.
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EXAMPLE
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Triangle begins:
1;
1, 2, 3;
3, 4, 6, 9, 12;
12, 15, 19, 25, 34, 46, 58;
58, 70, 85, 104, 129, 163, 209, 267, 325;
325, 383, 453, 538, 642, 771, 934, 1143, 1410, 1735, 2060;
2060, 2385, 2768, 3221, 3759, 4401, 5172, 6106, 7249, 8659, 10394, 12454, 14514; ...
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PROGRAM
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(PARI) {T(n, k)=local(A=1]); if(2*n<k|k<0, 0, if(n==0, 1, for(i=1, n, A=Vec(Ser(concat(concat(A[ #A], A), A[ #A]))/(1-x))); A[k+1]))}
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CROSSREFS
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Cf. A132290 (main diagonal), A125276 (column 0).
Sequence in context: A091275 A046936 A017831 this_sequence A078467 A154217 A049790
Adjacent sequences: A132286 A132287 A132288 this_sequence A132290 A132291 A132292
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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), Aug 18 2007
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