A148562 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, 0, 1), (0, 1, -1), (1, 0, -1)}.

1, 1, 3, 6, 18, 51, 155, 506, 1627, 5553, 19155, 66805, 240211, 863960, 3165182, 11733955, 43652243, 164830834, 624894684, 2385717893, 9190397204, 35493497563, 138120244600, 539990789121, 2118183372082, 8359695002728, 33079605209574, 131427000239706, 524324934717073, 2096414972054403

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, 1 + k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[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: A148560 A148561 A123891 * A148563 A148564 A148565

Adjacent sequences: A148559 A148560 A148561 * A148563 A148564 A148565

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved