A148686 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), (0, 0, -1), (1, -1, -1), (1, 1, 0)}.

1, 1, 3, 7, 22, 67, 228, 775, 2787, 10096, 37692, 142300, 546739, 2124319, 8349915, 33135509, 132647446, 535088379, 2174051788, 8887400681, 36550977240, 151088635064, 627703523526, 2619294449873, 10975951665533, 46172369684781, 194925589213610, 825737811918024, 3508786527526401

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[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: A365452 A035353 A242566 * A148687 A319312 A325213

Adjacent sequences: A148683 A148684 A148685 * A148687 A148688 A148689

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved