A150302 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, 0), (1, -1, -1), (1, 0, 0), (1, 1, 0)}.

1, 2, 7, 21, 80, 281, 1138, 4369, 18302, 73789, 315759, 1314708, 5718763, 24368034, 107302457, 464979845, 2066691614, 9071525567, 40625817135, 180148052526, 811809392966, 3629460525990, 16440663433625, 73999782874666, 336685091247671, 1523982877313501, 6960274780373417, 31655866376913556

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, -1 + j, k, -1 + n] + aux[-1 + i, j, k, -1 + n] + aux[-1 + i, 1 + j, 1 + k, -1 + n] + aux[1 + i, j, 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: A151289 A150300 A150301 * A150303 A150304 A150305

Adjacent sequences: A150299 A150300 A150301 * A150303 A150304 A150305

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved