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A113953
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A Jacobsthal matrix.
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2
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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; refs; listen; history; internal format)
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OFFSET
| 0,5
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COMMENTS
| 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
| 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
| 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
| Sequence in context: A071920 A065719 A204387 * A110509 A204040 A089975
Adjacent sequences: A113950 A113951 A113952 * A113954 A113955 A113956
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KEYWORD
| easy,nonn,tabl
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Nov 09 2005
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