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A149618 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), (-1, 1, 1), (1, 0, -1), (1, 1, 1)} 0
1, 1, 5, 15, 65, 231, 1077, 4077, 19521, 77847, 375523, 1542669, 7503275, 31482945, 153831367, 656080547, 3217363353, 13890626113, 68303798347, 297856509483, 1467615828795, 6451956824907, 31844333302963, 140944569490221, 696579282949195, 3100862322964479, 15342444196387139, 68634610543557457 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..27.

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, 1 + k, -1 + n] + aux[1 + i, -1 + 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: A189945 A066886 A149617 * A323793 A149619 A149620

Adjacent sequences:  A149615 A149616 A149617 * A149619 A149620 A149621

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved

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Last modified October 17 02:45 EDT 2021. Contains 348048 sequences. (Running on oeis4.)