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A148780 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, 0), (-1, 1, -1), (0, 0, -1), (0, 1, 1), (1, -1, 0)} 0
1, 1, 3, 8, 23, 81, 280, 961, 3559, 13454, 50692, 196368, 776979, 3070167, 12268437, 49815796, 203119103, 831940820, 3442970866, 14329445203, 59783757046, 250943394923, 1059386977640, 4484344952953, 19051650390329, 81318085577387, 348069408274893, 1493378869048524, 6429188146005489 (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[i, -1 + j, -1 + k, -1 + n] + aux[i, j, 1 + k, -1 + n] + aux[1 + i, -1 + j, 1 + k, -1 + n] + aux[1 + i, 1 + j, 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: A321730 A047143 A148779 * A148781 A327151 A317362

Adjacent sequences:  A148777 A148778 A148779 * A148781 A148782 A148783

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved

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Last modified January 27 09:44 EST 2022. Contains 350607 sequences. (Running on oeis4.)