A149180 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, 0), (0, 1, -1), (1, -1, 0), (1, 1, 0)}.

1, 1, 4, 10, 36, 119, 453, 1691, 6640, 26444, 107761, 445570, 1866616, 7916881, 33923740, 146666902, 639199703, 2805469930, 12395141339, 55081556226, 246070109241, 1104581807481, 4980421002183, 22548365703429, 102469842575184, 467289169399463, 2137858084475851, 9810302922185990

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, 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, -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: A358212 A088013 A149179 * A149181 A149182 A149183

Adjacent sequences: A149177 A149178 A149179 * A149181 A149182 A149183

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved