A148537 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), (0, 0, -1), (0, 1, 1), (1, -1, -1)}.

1, 1, 3, 5, 19, 45, 161, 457, 1571, 5133, 17539, 60615, 210997, 744557, 2682465, 9596691, 35214755, 128039943, 473335939, 1758472503, 6539815607, 24610987311, 92318357155, 349482079913, 1327838985311, 5049241556553, 19348234377367, 74002908443465, 284803026049073, 1098770756946235, 4242810322978199

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[i, -1 + j, -1 + k, -1 + n] + aux[i, 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: A148534 A148535 A148536 * A148538 A148539 A148540

Adjacent sequences: A148534 A148535 A148536 * A148538 A148539 A148540

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved