A150501 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), (1, -1, 1), (1, 0, 1), (1, 1, 0)}.

1, 2, 7, 25, 102, 403, 1713, 7182, 31386, 135608, 602264, 2654258, 11926855, 53294536, 241519429, 1089964398, 4972116229, 22612082186, 103690698286, 474386571094, 2184669741362, 10043510005574, 46417678346913, 214246192924683, 993160159767510, 4599387033904973, 21376180452440544, 99276104108734781

Offset

0,2

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, j, -1 + k, -1 + n] + aux[-1 + 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: A150499 A150500 A221455 * A150502 A150503 A150504

Adjacent sequences: A150498 A150499 A150500 * A150502 A150503 A150504

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved