A148017 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, 1, 0), (0, 1, -1), (1, 0, 0)}.

1, 1, 2, 3, 8, 17, 46, 117, 365, 1038, 3155, 9720, 31261, 99782, 322517, 1078436, 3639101, 12237485, 41922026, 146103022, 508439432, 1781167516, 6315381661, 22553829270, 80707216930, 290156888459, 1053694190563, 3840261414949, 14000670459904, 51441715144852, 190036544389434, 702284944553435, 2606556569184976

Offset

0,3

Links

Table of n, a(n) for n=0..32.

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, j, k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + 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]]; Table[Sum[aux[i, j, k, n], {i, 0, n}, {j, 0, n}, {k, 0, n}], {n, 0, 10}]

Crossrefs

Sequence in context: A148014 A148015 A148016 * A148018 A148019 A148020

Adjacent sequences: A148014 A148015 A148016 * A148018 A148019 A148020

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved