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A151021 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, 0, 0), (1, -1, 0), (1, 1, 0), (1, 1, 1)} 0
1, 2, 10, 36, 172, 728, 3464, 15568, 74544, 344736, 1661120, 7813024, 37832352, 179948288, 874662336, 4193406912, 20443796032, 98592134144, 481820595712, 2334160892160, 11429701284096, 55569137960192, 272556972992768, 1328958266428416, 6527479856821248, 31903065081293824, 156888633418270720 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..26.

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, -1 + j, k, -1 + n] + aux[-1 + i, 1 + j, k, -1 + n] + aux[1 + i, j, 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: A026546 A256105 A151020 * A151022 A144895 A236767

Adjacent sequences:  A151018 A151019 A151020 * A151022 A151023 A151024

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved

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Last modified November 16 17:33 EST 2019. Contains 329201 sequences. (Running on oeis4.)