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A091597
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Triangle read by rows: T(n,0)=A001045(n), T(n,m)=T(n-1,m-1)+T(n-1,m).
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2
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1, 1, 1, 3, 2, 1, 5, 5, 3, 1, 11, 10, 8, 4, 1, 21, 21, 18, 12, 5, 1, 43, 42, 39, 30, 17, 6, 1, 85, 85, 81, 69, 47, 23, 7, 1, 171, 170, 166, 150, 116, 70, 30, 8, 1, 341, 341, 336, 316, 266, 186, 100, 38, 9, 1, 683, 682, 677, 652, 582, 452, 286, 138, 47, 10, 1, 1365, 1359, 1329
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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COMMENTS
| A Jacobsthal-Pascal triangle.
Equals triangle M * Pascal's triangle, M = an infinite lower triangular Toeplitz matrix with A078008: [1, 0, 2, 2, 6, 10, 22, 42,...] in every column. [From Gary W. Adamson (qntmpkt(AT)yahoo.com), May 25 2009]
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FORMULA
| Number triangle T(n, k)=sum{j=0..n, binomial(n-j, k+j)2^j}; Riordan array (1/(1-x-2x^2), x/(1-x)); k-th column has g.f. (1/(1-x-2x^2))(x/(1-x))^k.
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EXAMPLE
| Rows start {1}, {1,1}, {3,2,1}, {5,5,3,1}, {11,10,8,4,1}...
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CROSSREFS
| Columns include A001045, A000975, A011377. Row sums are A059570.
A078008 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), May 25 2009]
Sequence in context: A080883 A021315 A068389 * A091595 A132969 A132970
Adjacent sequences: A091594 A091595 A091596 * A091598 A091599 A091600
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KEYWORD
| easy,nonn,tabl
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Jan 23 2004
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