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A144447
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Four term recursive triangular sequence: A(n,k)= A(n - 1, k - 1) + A(n - 1, k) + A(n - 2, k - 1) + A(n, k - 1).
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0
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1, 1, 1, 1, 4, 1, 1, 7, 13, 1, 1, 10, 34, 49, 1, 1, 13, 64, 160, 211, 1, 1, 16, 103, 361, 781, 994, 1, 1, 19, 151, 679, 1981, 3967, 4963, 1, 1, 22, 208, 1141, 4162, 10891, 20815, 25780, 1, 1, 25, 274, 1774, 7756, 24790, 60463, 112021, 137803, 1
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,5
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COMMENTS
| Row sums are:{1, 2, 6, 22, 95, 450, 2257, 11762, 63021, 344908}.
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FORMULA
| A(n,k)= A(n - 1, k - 1) + A(n - 1, k) + A(n - 2, k - 1) + A(n, k - 1).
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EXAMPLE
| {1},
{1, 1},
{1, 4, 1},
{1, 7, 13, 1},
{1, 10, 34, 49, 1},
{1, 13, 64, 160, 211, 1},
{1, 16, 103, 361, 781, 994, 1},
{1, 19, 151, 679, 1981, 3967, 4963, 1},
{1, 22, 208, 1141, 4162, 10891, 20815, 25780, 1},
{1, 25, 274, 1774, 7756, 24790, 60463, 112021, 137803, 1}
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MATHEMATICA
| Clear[A, n, k] A[n_, 1] := 1; A[n_, n_] := 1; A[n_, k_] := A[n - 1, k - 1] + A[n - 1, k] + A[n - 2, k - 1] + A[n, k - 1]; a = Table[A[n, k], {n, 10}, {k, n}]; Flatten[a]
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CROSSREFS
| Sequence in context: A073697 A193636 A119673 * A051455 A158687 A141541
Adjacent sequences: A144444 A144445 A144446 * A144448 A144449 A144450
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KEYWORD
| nonn,uned
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AUTHOR
| Roger L. Bagula and Gary W. Adamson (rlbagulatftn(AT)yahoo.com), Oct 05 2008
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