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A149136 Number of walks within N^3 (the first octant of Z^3) starting at (0,0,0) and consisting of n steps taken from {(-1, -1, 1), (-1, 0, 0), (0, -1, 1), (1, -1, -1), (1, 1, 0)}. 0
1, 1, 4, 9, 34, 114, 412, 1525, 5750, 22180, 87212, 344932, 1378350, 5559474, 22587780, 92430941, 380169394, 1570761624, 6519130912, 27166630828, 113611754346, 476626237184, 2005234655498, 8458477866254, 35766576196524, 151574472175434, 643662078045994, 2738451648287230, 11671117825365286 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..28.

A. Bostan and M. Kauers, 2008. Automatic Classification of Restricted Lattice Walks, ArXiv 0811.2899.

MATHEMATICA

aux[i_Integer, j_Integer, k_Integer, n_Integer] := Which[Min[i, j, k, n] < 0 || Max[i, j, k] > n, 0, n == 0, KroneckerDelta[i, j, k, n], True, aux[i, j, k, n] = aux[-1 + i, -1 + j, k, -1 + n] + aux[-1 + i, 1 + j, 1 + k, -1 + n] + aux[i, 1 + j, -1 + k, -1 + n] + aux[1 + i, j, k, -1 + n] + aux[1 + i, 1 + j, -1 + k, -1 + n]]; Table[Sum[aux[i, j, k, n], {i, 0, n}, {j, 0, n}, {k, 0, n}], {n, 0, 10}]

CROSSREFS

Sequence in context: A149133 A149134 A149135 * A006392 A179079 A084449

Adjacent sequences:  A149133 A149134 A149135 * A149137 A149138 A149139

KEYWORD

nonn,walk,changed

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved

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Last modified January 26 22:05 EST 2022. Contains 350601 sequences. (Running on oeis4.)