A149672 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), (0, -1, 0), (0, 1, -1), (1, 1, 1)}.

1, 1, 5, 17, 65, 253, 1071, 4469, 18995, 82111, 359215, 1581495, 7010885, 31284419, 140356821, 632723871, 2863416051, 13002311353, 59240248483, 270728014969, 1240386485657, 5695744333945, 26211915574453, 120875008483619, 558420257834857, 2583981455639041, 11975292029692161, 55580014426467833

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, -1 + k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[i, 1 + j, 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: A120893 A195531 A273535 * A149673 A046231 A092896

Adjacent sequences: A149669 A149670 A149671 * A149673 A149674 A149675

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved