A148383 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, 0, -1), (0, 1, 0), (1, -1, 1)}.

1, 1, 2, 5, 16, 50, 155, 520, 1852, 6689, 24152, 88895, 336276, 1290375, 4970796, 19272883, 75691051, 300545743, 1199594439, 4804949939, 19368329062, 78661855921, 321113507062, 1314680128753, 5401412322285, 22300830778267, 92477666047975, 384557465300678, 1602917291647183, 6702572454835313

Offset

0,3

Links

Table of n, a(n) for n=0..29.

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[i, -1 + j, k, -1 + n] + aux[i, j, 1 + 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: A334293 A278274 A148382 * A148384 A148385 A205501

Adjacent sequences: A148380 A148381 A148382 * A148384 A148385 A148386

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved