A151186 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), (0, 0, 1), (0, 1, -1), (1, 0, 0), (1, 1, 1)}

1, 3, 12, 51, 228, 1049, 4912, 23310, 111611, 538350, 2611000, 12719428, 62181672, 304871715, 1498393712, 7379275195, 36403845579, 179852166090, 889676649510, 4405782364400, 21838700181353, 108340738964579, 537866816660190, 2672014854526180, 13281659061969012, 66052268381557539, 328640757399863619

Offset

0,2

Links

Table of n, a(n) for n=0..26.

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[-1 + i, j, k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[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: A151184 A256334 A151185 * A151187 A340893 A151188

Adjacent sequences: A151183 A151184 A151185 * A151187 A151188 A151189

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved