A149318 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), (0, 0, -1), (0, 1, -1), (1, 0, 1)}.

1, 1, 4, 12, 35, 137, 495, 1729, 7098, 27593, 104531, 441615, 1789017, 7095763, 30558979, 127135970, 519443108, 2268126113, 9614119097, 40107736971, 176961174469, 760585348983, 3222491238945, 14334497855854, 62275808514893, 267036125594002, 1195679239707388, 5239373610306369

Offset

0,3

Links

Table of n, a(n) for n=0..27.

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, -1 + j, 1 + k, -1 + n] + aux[i, 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: A196859 A090328 A200541 * A233181 A053595 A300553

Adjacent sequences: A149315 A149316 A149317 * A149319 A149320 A149321

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved