A148369 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, 1, -1), (-1, 1, 0), (0, 1, 1), (1, -1, 0)}.

1, 1, 2, 5, 16, 42, 147, 454, 1628, 5425, 20178, 70153, 268235, 962420, 3748820, 13809050, 54492862, 204977746, 817599476, 3126108027, 12586411942, 48758462507, 197878414706, 775091653268, 3166333356578, 12521930286700, 51439036172347, 205114689753037, 846727775491103, 3400496099226738

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, k, -1 + n] + aux[i, -1 + 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, 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: A163825 A102866 A148368 * A148370 A148371 A148372

Adjacent sequences: A148366 A148367 A148368 * A148370 A148371 A148372

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved