A151020 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, -1, 0), (1, 1, 0), (1, 1, 1)}.

1, 2, 10, 36, 168, 720, 3304, 15088, 69904, 326624, 1535040, 7251968, 34448064, 164071424, 784830976, 3762710272, 18090215424, 87167033856, 420815500544, 2035432822272, 9860443239424, 47839254740992, 232412062604288, 1130458029407232, 5504894214334464, 26834127921946624, 130931569849067520

Offset

0,2

Links

Table of n, a(n) for n=0..26.

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, -1 + j, k, -1 + n] + aux[i, 1 + j, 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: A370713 A026546 A256105 * A151021 A151022 A144895

Adjacent sequences: A151017 A151018 A151019 * A151021 A151022 A151023

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved