A148802 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, 0, 1), (0, -1, 1), (0, 1, -1), (1, 0, 1)}.

1, 1, 3, 8, 26, 80, 277, 930, 3318, 11643, 42412, 152958, 565237, 2075930, 7753263, 28843854, 108607503, 407906636, 1545829275, 5848333453, 22278963147, 84775245709, 324339392219, 1239936468371, 4760994836197, 18271315079302, 70372359435245, 270943377363634, 1046308088337600, 4039544714639796

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, j, -1 + k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[i, 1 + j, -1 + k, -1 + n] + aux[1 + i, 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: A131910 A205775 A331320 * A255712 A194690 A148803

Adjacent sequences: A148799 A148800 A148801 * A148803 A148804 A148805

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved