A150446 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, 1), (1, 0, -1), (1, 0, 0), (1, 0, 1)}.

1, 2, 7, 24, 102, 417, 1870, 8084, 37470, 168965, 794731, 3654241, 17409564, 81476048, 390757848, 1846159739, 8911674092, 42495832330, 205901393430, 987251611544, 4801802056122, 23152006338312, 112876113393819, 546156268722029, 2669431334997184, 12963330205039792, 63465753054060682, 308954533070833734

Offset

0,2

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[-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, -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: A150443 A150444 A150445 * A150447 A150448 A256492

Adjacent sequences: A150443 A150444 A150445 * A150447 A150448 A150449

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved