A149898 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, 1, 1), (0, 0, 1), (0, 1, 0), (1, 0, -1)}.

1, 2, 5, 14, 46, 163, 604, 2312, 9096, 36618, 150109, 624637, 2632371, 11214343, 48222612, 209038216, 912561043, 4008715175, 17707364850, 78605026891, 350490038669, 1569073486654, 7050036268911, 31781800472145, 143708009436873, 651613553588894, 2962168943627220, 13497542814094082

Offset

0,2

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[i, -1 + j, k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[1 + i, -1 + j, -1 + 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: A149896 A149897 A124527 * A240611 A240612 A240613

Adjacent sequences: A149895 A149896 A149897 * A149899 A149900 A149901

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved