A151105 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), (0, 0, 1), (0, 1, 0), (1, 1, -1), (1, 1, 0)}.

1, 3, 11, 44, 185, 804, 3576, 16179, 74162, 343463, 1603908, 7541122, 35658174, 169421084, 808274631, 3869817810, 18585058316, 89498454123, 432024934133, 2089915753028, 10129261019930, 49178146380312, 239133208092212, 1164443575855438, 5677449527001260, 27713829071829689, 135427236840563801

Offset

0,2

Links

Table of n, a(n) for n=0..26.

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[i, -1 + j, k, -1 + n] + aux[i, j, -1 + 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: A132840 A091200 A271931 * A127632 A061706 A361764

Adjacent sequences: A151102 A151103 A151104 * A151106 A151107 A151108

Keyword

nonn,walk,changed

Author

Manuel Kauers, Nov 18 2008

Status

approved