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A142596 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). 0
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,5

COMMENTS

Row sums are:

{1, 2, 8, 44, 260, 1556, 9332, 55988, 335924, 2015540}.

This triangle sequence is internally lower than the MacMahon type A060187.

LINKS

Table of n, a(n) for n=1..52.

FORMULA

t(n,k)=t(n - 1, k - 1) + 3* t(n - 1, k) + 2*t(n - 1, k - 1).

EXAMPLE

{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}

MATHEMATICA

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]

CROSSREFS

Cf. A008292, A119258, A060187.

Sequence in context: A296827 A056941 A157638 * A176063 A155467 A152936

Adjacent sequences:  A142593 A142594 A142595 * A142597 A142598 A142599

KEYWORD

nonn,uned

AUTHOR

Roger L. Bagula, Sep 22 2008

STATUS

approved

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Last modified January 18 00:56 EST 2021. Contains 340249 sequences. (Running on oeis4.)