A151023 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, 0, 0), (-1, 0, 1), (0, -1, 0), (1, 1, 0), (1, 1, 1)}.

1, 2, 10, 40, 176, 808, 3720, 17152, 81440, 384448, 1824448, 8758400, 42003840, 201892480, 977114240, 4726665216, 22901914112, 111430159360, 542141168640, 2640679776256, 12898118598656, 63006347137024, 308047467597824, 1509004351340544, 7393407993561088, 36248756250542080, 177971449582911488

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, -1 + k, -1 + n] + aux[1 + i, 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: A223095 A052978 A351511 * A344501 A151024 A151025

Adjacent sequences: A151020 A151021 A151022 * A151024 A151025 A151026

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved