A150732 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), (0, 0, -1), (0, 1, 1), (1, 0, 1), (1, 1, -1)}.

1, 2, 8, 28, 130, 542, 2584, 11496, 55678, 256510, 1254108, 5903846, 29033776, 138631022, 684430494, 3300277738, 16338765082, 79346440476, 393614695616, 1921710776096, 9547446375432, 46802969161876, 232795453464222, 1144840179066616, 5699509516958702, 28100203500809862, 139994900695963422

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, -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: A150730 A307940 A150731 * A225689 A330211 A216785

Adjacent sequences: A150729 A150730 A150731 * A150733 A150734 A150735

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved