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A142596
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Symmetrical recursion of the Pascal triangle type ( MacMahon like): t(n,k)=t(n - 1, k - 1) + 3* t(n - 1, k) + 2*t(n - 1, k - 1).
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0
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1, 1, 1, 1, 6, 1, 1, 21, 21, 1, 1, 66, 126, 66, 1, 1, 201, 576, 576, 201, 1, 1, 606, 2331, 3456, 2331, 606, 1, 1, 1821, 8811, 17361, 17361, 8811, 1821, 1, 1, 5466, 31896, 78516, 104166, 78516, 31896, 5466, 1, 1, 16401, 112086, 331236, 548046, 548046, 331236
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OFFSET
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1,5
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COMMENTS
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Row sums are:
{1, 2, 8, 44, 260, 1556, 9332, 55988, 335924, 2015540}.
This triangle sequence is internally lower than the MacMahon type A060187.
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LINKS
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Table of n, a(n) for n=1..52.
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FORMULA
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t(n,k)=t(n - 1, k - 1) + 3* t(n - 1, k) + 2*t(n - 1, k - 1).
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EXAMPLE
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{1},
{1, 1},
{1, 6, 1},
{1, 21, 21, 1},
{1, 66, 126, 66, 1},
{1, 201, 576, 576, 201, 1},
{1, 606, 2331, 3456, 2331, 606, 1},
{1, 1821, 8811, 17361, 17361, 8811, 1821, 1},
{1, 5466, 31896, 78516, 104166, 78516, 31896, 5466, 1},
{1, 16401, 112086, 331236, 548046, 548046, 331236, 112086, 16401, 1}
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MATHEMATICA
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A[n_, 1] := 1 A[n_, n_] := 1 A[n_, k_] := A[n - 1, k - 1] + 3* A[n - 1, k] + 2*A[n - 1, k - 1]; a = Table[A[n, k], {n, 10}, {k, n}]; Flatten[a]
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CROSSREFS
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Cf. A008292, A119258, A060187.
Sequence in context: A296827 A056941 A157638 * A176063 A155467 A152936
Adjacent sequences: A142593 A142594 A142595 * A142597 A142598 A142599
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KEYWORD
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nonn,uned
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AUTHOR
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Roger L. Bagula, Sep 22 2008
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STATUS
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approved
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