A148213 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, 0, -1), (0, 0, 1), (1, 1, -1)}.

1, 1, 2, 4, 13, 31, 89, 263, 849, 2489, 7948, 26132, 85913, 276811, 935850, 3195236, 10784937, 36653147, 127830808, 444962432, 1541290899, 5409570385, 19197622065, 67828393121, 240141102163, 859491924151, 3085139246610, 11048840438098, 39776670165439, 144121126222677, 522104131067377, 1892475604692523

Offset

0,3

Links

Table of n, a(n) for n=0..31.

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, j, -1 + k, -1 + n] + aux[1 + i, 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: A034500 A261455 A077325 * A148214 A148215 A148216

Adjacent sequences: A148210 A148211 A148212 * A148214 A148215 A148216

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved