A151078 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, 0), (0, 1, 0), (1, 0, 1), (1, 1, 0)}.

1, 3, 10, 41, 168, 717, 3171, 14064, 63793, 291614, 1342355, 6241899, 29121390, 136728440, 644720130, 3049649696, 14485085422, 68965374343, 329289549850, 1576109416647, 7558354053698, 36324991365101, 174860231643710, 843127328761125, 4071533539551152, 19687239798248824, 95321169488056293

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, j, -1 + k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[1 + i, 1 + 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: A149056 A149057 A149058 * A151079 A151080 A153474

Adjacent sequences: A151075 A151076 A151077 * A151079 A151080 A151081

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved