A150109 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), (-1, 1, 1), (0, 0, 1), (0, 1, -1), (1, 0, 0)}.

1, 2, 6, 19, 69, 263, 1044, 4240, 17595, 74391, 318493, 1378895, 6022039, 26520440, 117549906, 524068965, 2348103782, 10568464412, 47754218422, 216537083286, 984983798215, 4493317804295, 20550859759855, 94213221969645, 432845203438126, 1992563341419802, 9189311952508953, 42450573153408853

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, k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[1 + i, -1 + 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: A150107 A148472 A150108 * A150110 A150111 A150112

Adjacent sequences: A150106 A150107 A150108 * A150110 A150111 A150112

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved