A149549 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, 0, 0), (-1, 0, 1), (1, -1, 0), (1, 1, 0)}

1, 1, 5, 13, 57, 185, 837, 2937, 13469, 50053, 231217, 890229, 4139401, 16354421, 76393849, 307792285, 1443118481, 5903933641, 27765120645, 115004559193, 542206182909, 2268903801801, 10719898112253, 45245504677105, 214162624027061, 910577580645457, 4316931291076229, 18471685550254169

Offset

0,3

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, -1 + j, k, -1 + n] + aux[-1 + i, 1 + j, k, -1 + n] + aux[1 + i, j, -1 + k, -1 + n] + aux[1 + i, j, 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: A176648 A159489 A353287 * A149550 A149551 A149552

Adjacent sequences: A149546 A149547 A149548 * A149550 A149551 A149552

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved