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Search: id:A123490
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| A123490 |
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Triangle whose k-th column satisfies a(n)=(k+3)*a(n-1)-(k+2)*a(n-2). |
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3
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| 1, 2, 1, 4, 2, 1, 8, 5, 2, 1, 16, 14, 6, 2, 1, 32, 41, 22, 7, 2, 1, 64, 122, 86, 32, 8, 2, 1, 128, 365, 342, 157, 44, 9, 2, 1, 256, 1094, 1366, 782, 260, 58, 10, 2, 1
(list; table; graph; listen)
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OFFSET
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0,2
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COMMENT
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Column k has g.f. x^k*(1-x(1+k))/((1-x)*(1-x(2+k))). Row sums are A103439. Columns include A000079,A007051,A047849,A047850,A047851. Diagonal sums are A123491.
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FORMULA
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Number triangle T(n,k)=[k<=n]*((k+2)^(n-k)+k)/(k+1)
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EXAMPLE
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Triangle begins
1,
2, 1,
4, 2, 1,
8, 5, 2, 1,
16, 14, 6, 2, 1,
32, 41, 22, 7, 2, 1,
64, 122, 86, 32, 8, 2, 1,
128, 365, 342, 157, 44, 9, 2, 1,
256, 1094, 1366, 782, 260, 58, 10, 2, 1,
512, 3281, 5462, 3907, 1556, 401, 74, 11, 2, 1,
1024, 9842, 21846, 19532, 9332, 2802, 586, 92, 12, 2, 1
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CROSSREFS
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Cf. A047848.
Sequence in context: A106471 A054453 A109433 this_sequence A157028 A060637 A123486
Adjacent sequences: A123487 A123488 A123489 this_sequence A123491 A123492 A123493
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KEYWORD
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easy,nonn,tabl
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AUTHOR
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Paul Barry (pbarry(AT)wit.ie), Oct 01 2006
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