A149141 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, 0), (-1, 0, 1), (1, -1, 1), (1, 1, 0)}.

1, 1, 4, 9, 36, 112, 444, 1547, 6307, 22910, 95780, 357505, 1516176, 5792384, 24759719, 96447614, 414381271, 1639048308, 7071067205, 28301323345, 122534510477, 495035478897, 2149926754862, 8752873856583, 38110447902053, 156185005509198, 681454240000859, 2808884587079844, 12276690255246744

Offset

0,3

Links

Table of n, a(n) for n=0..28.

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, k, -1 + n] + aux[-1 + i, 1 + j, -1 + k, -1 + n] + aux[1 + i, j, -1 + k, -1 + n] + aux[1 + i, 1 + j, 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: A149139 A149140 A239230 * A149142 A149143 A149144

Adjacent sequences: A149138 A149139 A149140 * A149142 A149143 A149144

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved