A150776 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, 1, -1), (1, 0, 1), (1, 1, 0)}

1, 2, 8, 30, 130, 564, 2548, 11632, 53966, 252352, 1190264, 5645555, 26918817, 128873295, 619197406, 2983890805, 14417128774, 69815452709, 338760986580, 1646644898893, 8016599685365, 39083397359719, 190786100724902, 932396821431482, 4561521975619923, 22337476999060381, 109481152344605996

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[i, -1 + 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: A150773 A150774 A150775 * A150777 A150778 A150779

Adjacent sequences: A150773 A150774 A150775 * A150777 A150778 A150779

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved