A150212 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, 0, 1), (0, 1, 0), (1, -1, 1), (1, 0, -1)}.

1, 2, 6, 21, 81, 331, 1405, 6134, 27331, 123742, 567304, 2627172, 12267169, 57671808, 272693750, 1295686844, 6182107658, 29603230521, 142201981662, 684965998290, 3307416586384, 16004684113039, 77596661917609, 376869159163474, 1833224367856779, 8930048599783207, 43556122332636789, 212692776891161612

Offset

0,2

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, j, 1 + k, -1 + n] + aux[-1 + i, 1 + j, -1 + k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[i, 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: A150211 A148493 A148494 * A150213 A279565 A150214

Adjacent sequences: A150209 A150210 A150211 * A150213 A150214 A150215

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved