A148023 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, 1, 0), (1, 0, -1), (1, 0, 0)}.

1, 1, 2, 3, 8, 17, 48, 112, 375, 995, 3275, 8876, 31891, 94113, 332788, 988399, 3711314, 11670675, 43086404, 135569589, 524171391, 1721594540, 6545887952, 21443044036, 84642973041, 286949416617, 1114660916146, 3762532807703, 15084773785655, 52390499421050, 206856697348630, 714656828323522, 2900243191235136

Offset

0,3

Links

Table of n, a(n) for n=0..32.

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, 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: A148020 A148021 A148022 * A148024 A148025 A324615

Adjacent sequences: A148020 A148021 A148022 * A148024 A148025 A148026

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved