A148225 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, -1), (0, 0, 1), (1, -1, -1), (1, 1, -1)}.

1, 1, 2, 4, 13, 31, 99, 291, 961, 3015, 10230, 34312, 119249, 409683, 1454025, 5182995, 18523533, 67012371, 245232291, 896656968, 3309285901, 12290521562, 45804467416, 171635860027, 645265019687, 2437630482990, 9249682909078, 35134037746185, 134114589749484, 513891798129711, 1969995320749982

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[-1 + i, 1 + j, 1 + k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[1 + i, 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: A148222 A148223 A148224 * A148226 A004644 A000866

Adjacent sequences: A148222 A148223 A148224 * A148226 A148227 A148228

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved