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A148136 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, 1), (1, 0, 0), (1, 1, -1)} 0
1, 1, 2, 4, 11, 28, 89, 258, 875, 2736, 9651, 31721, 114934, 391219, 1444642, 5045155, 18889869, 67267567, 254499953, 920173993, 3509555190, 12844126821, 49300579903, 182216041272, 703004670539, 2619545716418, 10148775007137, 38074615959324, 148021689616412, 558529113424010, 2177671784821983 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..30.

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, 1 + k, -1 + n] + aux[-1 + i, j, k, -1 + n] + aux[1 + i, j, -1 + 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: A151425 A148135 A034768 * A148137 A148138 A005503

Adjacent sequences:  A148133 A148134 A148135 * A148137 A148138 A148139

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved

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Last modified September 25 00:48 EDT 2020. Contains 337333 sequences. (Running on oeis4.)