A150729 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), (0, 0, -1), (0, 1, 1), (1, 0, 1), (1, 1, -1)}.

1, 2, 8, 28, 126, 532, 2402, 10814, 49820, 231120, 1084480, 5112302, 24256900, 115558824, 552915824, 2654606230, 12783718698, 61715592848, 298622111154, 1447810307570, 7032313874674, 34213054744236, 166692061932344, 813209660021612, 3971961198887714, 19421367783963108, 95058408541332056

Offset

0,2

Links

Table of n, a(n) for n=0..26.

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, 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, 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: A150726 A150727 A150728 * A075662 A150730 A307940

Adjacent sequences: A150726 A150727 A150728 * A150730 A150731 A150732

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved