A148233 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, 1, 0), (1, -1, 1), (1, 0, -1), (1, 0, 0)}.

1, 1, 2, 4, 13, 34, 115, 358, 1305, 4394, 16799, 60226, 236724, 886170, 3571278, 13795768, 56634827, 224397093, 934699703, 3777744516, 15931909849, 65442228175, 278812189001, 1160886944859, 4988775300686, 21009096849154, 90962617263757, 386809467979266, 1685635564629301, 7228530971210101

Offset

0,3

Links

Table of n, a(n) for n=0..29.

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, k, -1 + n] + aux[-1 + i, j, 1 + k, -1 + n] + aux[-1 + i, 1 + j, -1 + k, -1 + n] + aux[1 + i, -1 + 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: A227808 A148231 A148232 * A148234 A284335 A192443

Adjacent sequences: A148230 A148231 A148232 * A148234 A148235 A148236

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved