A151245 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), (0, 1, 0), (0, 1, 1), (1, 0, 0), (1, 0, 1)}.

1, 4, 16, 72, 336, 1568, 7488, 36160, 174720, 851456, 4169728, 20430848, 100515840, 495792128, 2446532608, 12099710976, 59931222016, 296944959488, 1473274707968, 7316502806528, 36344236736512, 180693350744064, 898922565861376, 4472907322884096, 22269415918665728, 110921723058061312

Offset

0,2

Links

Table of n, a(n) for n=0..25.

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[i, -1 + j, -1 + k, -1 + n] + aux[i, -1 + 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: A180141 A226282 A013991 * A151246 A152807 A217461

Adjacent sequences: A151242 A151243 A151244 * A151246 A151247 A151248

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved