A149530 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), (-1, 1, 1), (1, -1, -1), (1, 1, 1)}

1, 1, 5, 11, 55, 167, 811, 2821, 13625, 50809, 246173, 958101, 4659993, 18686581, 91153825, 373735743, 1827361155, 7621127667, 37337909095, 157839116035, 774611283687, 3310847912475, 16271418253807, 70189445466941, 345367689160737, 1501420646123219, 7395475289673823, 32365159604914277

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[1 + i, -1 + 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: A028349 A149528 A149529 * A149531 A083860 A141496

Adjacent sequences: A149527 A149528 A149529 * A149531 A149532 A149533

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved