A148260 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, -1), (-1, -1, 0), (-1, 1, -1), (0, 1, 0), (1, -1, 1)}.

1, 1, 2, 4, 14, 33, 111, 303, 1110, 3208, 12008, 36659, 140407, 443934, 1728381, 5621637, 22157625, 73695819, 293433309, 993846730, 3989790974, 13719801711, 55458702423, 193168626049, 785413014326, 2765967573176, 11302988484052, 40187871318426, 164946452733297, 591408009949277, 2436722533087948

Offset

0,3

Links

Table of n, a(n) for n=0..30.

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[1 + i, -1 + j, 1 + k, -1 + n] + aux[1 + i, 1 + j, k, -1 + n] + aux[1 + i, 1 + j, 1 + 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: A148257 A148258 A148259 * A148261 A148262 A148263

Adjacent sequences: A148257 A148258 A148259 * A148261 A148262 A148263

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved