A150819 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), (-1, 0, 1), (1, 0, -1), (1, 0, 0), (1, 1, 1)}

1, 2, 8, 31, 139, 596, 2778, 12535, 59457, 275768, 1322082, 6235333, 30105107, 143572987, 696651803, 3348513885, 16308045874, 78838993544, 385062407686, 1869708253006, 9152716474100, 44594412858807, 218705470159331, 1068511404790721, 5248379779402607, 25698823977875098, 126392797967659657

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, k, -1 + n] + aux[-1 + i, j, 1 + k, -1 + n] + aux[1 + 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: A150817 A150818 A009567 * A003175 A129427 A150820

Adjacent sequences: A150816 A150817 A150818 * A150820 A150821 A150822

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved