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A149043 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), (0, 1, 1), (1, -1, 0), (1, 1, -1)} 0
1, 1, 3, 10, 37, 134, 536, 2162, 9124, 38480, 165534, 723098, 3193196, 14221802, 63772316, 287880505, 1309694973, 5985175167, 27484724851, 126726210253, 586613118924, 2726313381339, 12707197416398, 59403354402305, 278452680056717, 1308485546821356, 6164054441335823, 29095697455150241 (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, 1 + j, k, -1 + n] + aux[i, -1 + j, -1 + 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: A080625 A289615 A138807 * A296000 A242725 A151315

Adjacent sequences:  A149040 A149041 A149042 * A149044 A149045 A149046

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved

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Last modified September 27 08:26 EDT 2020. Contains 337380 sequences. (Running on oeis4.)