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Search: id:A130456
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| A130456 |
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Triangle, read by rows of 2n+1 terms, where row n+1 is generated by taking partial sums of row n and then append a zero followed by the final term in the partial sums of row n, for n>=0, with T(0,0)=1. |
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+0
2
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| 1, 1, 0, 1, 1, 1, 2, 0, 2, 1, 2, 4, 4, 6, 0, 6, 1, 3, 7, 11, 17, 17, 23, 0, 23, 1, 4, 11, 22, 39, 56, 79, 79, 102, 0, 102, 1, 5, 16, 38, 77, 133, 212, 291, 393, 393, 495, 0, 495, 1, 6, 22, 60, 137, 270, 482, 773, 1166, 1559, 2054, 2054, 2549, 0, 2549, 1, 7, 29, 89, 226, 496, 978
(list; table; graph; listen)
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OFFSET
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0,7
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COMMENT
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Final term in row n equals A098746(n) = number of permutations of [1..n] which avoid 4231 and 42513.
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EXAMPLE
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Triangle begins:
1;
1, 0, 1;
1, 1, 2, 0, 2;
1, 2, 4, 4, 6, 0, 6;
1, 3, 7, 11, 17, 17, 23, 0, 23;
1, 4, 11, 22, 39, 56, 79, 79, 102, 0, 102;
1, 5, 16, 38, 77, 133, 212, 291, 393, 393, 495, 0, 495;
1, 6, 22, 60, 137, 270, 482, 773, 1166, 1559, 2054, 2054, 2549, 0, 2549; ...
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PROGRAM
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(PARI) {T(n, k)=local(A=[1], B); if(n==0, if(k==0, 1, 0), for(j=1, n, B=Vec(Ser(A)/(1-x)); A=concat(concat(B, 0), B[ #B])); A[k+1])}
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CROSSREFS
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Cf. A098746 (final term in rows).
Sequence in context: A125922 A076608 A068461 this_sequence A071497 A125939 A125942
Adjacent sequences: A130453 A130454 A130455 this_sequence A130457 A130458 A130459
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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), May 26 2007
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