A148041 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, 1), (-1, 1, 0), (0, 0, -1), (1, 0, 0), (1, 1, -1)}.

1, 1, 2, 3, 8, 19, 57, 158, 498, 1539, 5153, 17072, 59518, 206979, 745464, 2692747, 9954863, 37024599, 139880339, 532405810, 2049337223, 7946429854, 31083121339, 122394588218, 485449765051, 1936684059573, 7774072536288, 31366998291556, 127230398294122, 518455863490298, 2122312706665651

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, 1 + k, -1 + n] + aux[-1 + i, j, k, -1 + n] + aux[i, j, 1 + k, -1 + n] + aux[1 + i, -1 + j, k, -1 + n] + aux[1 + i, 1 + j, -1 + 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: A326301 A148039 A148040 * A148042 A077269 A294431

Adjacent sequences: A148038 A148039 A148040 * A148042 A148043 A148044

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved