A148201 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, 1), (0, -1, 1), (0, 1, 0), (1, 1, -1)}.

1, 1, 2, 4, 12, 34, 115, 381, 1382, 5021, 19107, 73516, 290271, 1160122, 4711298, 19347457, 80345025, 336732077, 1423193019, 6060568351, 25982989222, 112079577365, 486135477158, 2119306304250, 9281909110795, 40825347704860, 180268378930116, 798880428292549, 3552224088304126

Offset

0,3

Links

Table of n, a(n) for n=0..28.

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, k, -1 + n] + aux[i, 1 + j, -1 + k, -1 + n] + aux[1 + i, j, -1 + 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: A001895 A267618 A148200 * A148202 A148203 A240904

Adjacent sequences: A148198 A148199 A148200 * A148202 A148203 A148204

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved