A149706 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), (0, 0, -1), (1, -1, 1), (1, 1, 1)}.

1, 1, 5, 17, 69, 287, 1251, 5447, 24355, 110025, 501753, 2304001, 10667681, 49643657, 232116329, 1090122563, 5139589835, 24307439967, 115304943979, 548451658359, 2614900096295, 12494033115055, 59816931734319, 286902445776199, 1378354318693731, 6632190230901283, 31957606532958647, 154192144947956607

Offset

0,3

Links

Table of n, a(n) for n=0..27.

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, -1 + k, -1 + n] + aux[i, j, 1 + 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: A149704 A273426 A149705 * A273763 A149707 A214003

Adjacent sequences: A149703 A149704 A149705 * A149707 A149708 A149709

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved