A150411 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, 1, 1), (0, 0, 1), (0, 1, -1), (1, 0, 1)}.

1, 2, 7, 24, 94, 378, 1575, 6667, 28738, 125344, 552033, 2449988, 10946580, 49178724, 221991504, 1006153452, 4576671364, 20883615820, 95560707553, 438371820246, 2015526223707, 9285903235502, 42861771274089, 198178839571629, 917752325039967, 4256197793358095, 19765117991324590, 91900267981592351

Offset

0,2

Links

Table of n, a(n) for n=0..27.

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, -1 + k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[1 + i, -1 + 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: A150408 A150409 A150410 * A150412 A150413 A150414

Adjacent sequences: A150408 A150409 A150410 * A150412 A150413 A150414

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved