A149063 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, 0, 0), (-1, 0, 1), (0, 1, 1), (1, -1, 1), (1, 0, -1)}.

1, 1, 3, 11, 40, 157, 640, 2674, 11491, 49979, 221091, 987439, 4452885, 20248676, 92654032, 426656333, 1974387106, 9178717874, 42844941074, 200702312923, 943274839096, 4446116168773, 21012818945005, 99550378029003, 472676077480605, 2248928525326327, 10720242118051543, 51190864620269582

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, j, 1 + k, -1 + n] + aux[-1 + i, 1 + j, -1 + k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[1 + i, j, -1 + k, -1 + n] + aux[1 + i, 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: A346194 A346317 A119375 * A242467 A149064 A149065

Adjacent sequences: A149060 A149061 A149062 * A149064 A149065 A149066

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved