A150600 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, 0), (0, 1, 1), (1, 0, -1), (1, 0, 1)}.

1, 2, 7, 27, 109, 462, 2021, 8957, 40478, 184607, 850670, 3949965, 18446391, 86653625, 408802335, 1936326814, 9203631648, 43874127953, 209728998818, 1004912328372, 4825390938764, 23215849225298, 111890312560604, 540135699843988, 2611244410884437, 12640886843737626, 61270116153307678

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, j, -1 + k, -1 + n] + aux[-1 + i, j, 1 + k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[1 + i, 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: A026759 A361778 A150599 * A005768 A150601 A150602

Adjacent sequences: A150597 A150598 A150599 * A150601 A150602 A150603

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved