A149551 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, 0, -1), (1, 1, 1)}

1, 1, 5, 13, 57, 191, 849, 3133, 14149, 54985, 251685, 1011503, 4674197, 19248263, 89544717, 375543783, 1756059813, 7469472419, 35073265951, 150881670271, 710878991207, 3086792918655, 14583788826779, 63824100859983, 302239470621285, 1331552970097311, 6318005925541503, 27994895845833517

Offset

0,3

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, -1 + j, -1 + k, -1 + n] + aux[-1 + i, 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: A353287 A149549 A149550 * A149552 A084136 A091147

Adjacent sequences: A149548 A149549 A149550 * A149552 A149553 A149554

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved