A148118 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), (-1, 1, -1), (0, 0, 1), (1, 0, -1)}.

1, 1, 2, 4, 11, 26, 70, 205, 596, 1752, 5449, 17424, 54722, 177079, 592755, 1962134, 6546075, 22465233, 77286652, 264757142, 923848587, 3261028077, 11438600315, 40466392606, 145203933975, 519739374933, 1862573733531, 6757029999080, 24577060492657, 89186378240635, 326267260068833, 1200908820870124

Offset

0,3

Links

Table of n, a(n) for n=0..31.

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, 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, 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: A240571 A151257 A148117 * A148119 A148120 A148121

Adjacent sequences: A148115 A148116 A148117 * A148119 A148120 A148121

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved