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Search: id:A113953
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| 1, 0, 1, 0, 2, 1, 0, 0, 4, 1, 0, 0, 4, 6, 1, 0, 0, 0, 12, 8, 1, 0, 0, 0, 8, 24, 10, 1, 0, 0, 0, 0, 32, 40, 12, 1, 0, 0, 0, 0, 16, 80, 60, 14, 1, 0, 0, 0, 0, 0, 80, 160, 84, 16, 1, 0, 0, 0, 0, 0, 32, 240, 280, 112, 18, 1, 0, 0, 0, 0, 0, 0, 192, 560, 448, 144, 20, 1, 0, 0, 0, 0, 0, 0, 64, 672
(list; table; graph; listen)
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OFFSET
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0,5
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COMMENT
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Rows sums are the Jacobsthal numbers A001045(n+1). Diagonal sums are the Padovan-Jacobsthal numbers A052947. Inverse is (1,xc(-2x)), c(x) the g.f. of A000108, with general term k*C(2n-k-1,n-k)(-2)^(n - k)/n. A signed version is A110509.
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FORMULA
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G.f. : 1/(1-xy(1+2x)); Riordan array (1, x(1+2x)); Number triangle T(n, k)=2^(n-k)*binomial(k, n-k).
T(n,k)=A026729(n,k)*2^(n-k) . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 22 2006
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EXAMPLE
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Rows begin
1;
0, 1;
0, 2, 1;
0, 0, 4, 1;
0, 0, 4, 6, 1;
0, 0, 0, 12, 8, 1;
0, 0, 0, 8, 24, 10, 1;
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CROSSREFS
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Sequence in context: A099423 A071920 A065719 this_sequence A110509 A089975 A034366
Adjacent sequences: A113950 A113951 A113952 this_sequence A113954 A113955 A113956
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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), Nov 09 2005
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