A150780 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, 0, 1), (1, 0, -1), (1, 0, 1), (1, 1, 0)}

1, 2, 8, 30, 133, 566, 2617, 11763, 55530, 256938, 1227867, 5781928, 27850891, 132672582, 642602461, 3085978055, 15007566746, 72497656217, 353657229891, 1716074631939, 8391740124484, 40861709568748, 200210893873034, 977590879486953, 4797722906700485, 23479286547998069, 115387185124601996

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, k, -1 + n] + aux[-1 + i, j, -1 + k, -1 + n] + aux[-1 + i, j, 1 + k, -1 + n] + aux[1 + i, 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: A150777 A150778 A150779 * A150781 A150782 A150783

Adjacent sequences: A150777 A150778 A150779 * A150781 A150782 A150783

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved