A148141 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, 0), (1, -1, -1), (1, -1, 0)}.

1, 1, 2, 4, 11, 29, 82, 260, 800, 2619, 8769, 30113, 104125, 368767, 1332471, 4812536, 17702055, 65889593, 246466567, 928990097, 3539220977, 13559356521, 52132706845, 202134499150, 787843395550, 3079707819226, 12103469128615, 47810755194976, 189383676751565, 752728794091617, 3005178777356037

Offset

0,3

Links

Table of n, a(n) for n=0..30.

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, 1 + j, 1 + k, -1 + n] + aux[i, -1 + j, 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: A148140 A328139 A369359 * A317879 A148142 A148143

Adjacent sequences: A148138 A148139 A148140 * A148142 A148143 A148144

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved