A148966 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), (1, -1, 1), (1, 1, -1), (1, 1, 0)}

1, 1, 3, 9, 31, 107, 396, 1458, 5540, 21033, 81293, 314027, 1225435, 4783122, 18789381, 73832583, 291304767, 1149836260, 4551057689, 18020509287, 71487440526, 283703124753, 1127378648910, 4481531060923, 17831655342761, 70972544638250, 282676397433776, 1126167707925430, 4488901984666613

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, 1 + 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: A130620 A202246 A225340 * A279971 A127927 A148967

Adjacent sequences: A148963 A148964 A148965 * A148967 A148968 A148969

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved