A148116 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, 0, 1), (0, 1, -1), (1, -1, 1), (1, 0, 0)}.

1, 1, 2, 4, 10, 30, 92, 308, 1063, 3780, 13953, 52464, 201883, 791572, 3147547, 12702666, 51861591, 213937957, 891232927, 3743220743, 15841828369, 67512847684, 289488115049, 1248410486220, 5411866349876, 23571957134751, 103123866691859, 452984148808815, 1997259430689696, 8836941466654388

Offset

0,3

Links

Table of n, a(n) for n=0..29.

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[-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, 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: A337675 A148115 A361758 * A149833 A026119 A149834

Adjacent sequences: A148113 A148114 A148115 * A148117 A148118 A148119

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved