A149192 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), (1, -1, 0), (1, 1, -1), (1, 1, 0)}.

1, 1, 4, 10, 38, 123, 493, 1807, 7496, 29400, 125564, 514621, 2245001, 9488604, 42075089, 181941417, 817228089, 3596501357, 16322969441, 72842426204, 333437372040, 1504895912513, 6938137755904, 31607538219604, 146610789828190, 673159600610476, 3138793839304676, 14508091716818350

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, 1 + k, -1 + n] + aux[-1 + i, 1 + j, 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: A220198 A197051 A149191 * A032123 A149193 A149194

Adjacent sequences: A149189 A149190 A149191 * A149193 A149194 A149195

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved