A148540 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, 1), (-1, 0, 0), (1, -1, -1), (1, 1, 0)}.

1, 1, 3, 5, 19, 45, 167, 443, 1687, 5081, 19851, 61949, 242911, 795239, 3205607, 10806745, 43543547, 149722163, 611995035, 2158558103, 8864811287, 31612799289, 130436796397, 473156526527, 1966155354111, 7206688904867, 29996095281917, 111044220066677, 464651051449543, 1737431367642797

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, -1 + j, k, -1 + n] + aux[-1 + i, 1 + j, 1 + k, -1 + n] + aux[1 + i, j, k, -1 + n] + aux[1 + i, 1 + j, -1 + 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: A148537 A148538 A148539 * A148541 A148542 A148543

Adjacent sequences: A148537 A148538 A148539 * A148541 A148542 A148543

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved