A148197 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, 0, 0), (0, -1, 1), (0, 1, 0), (1, 1, -1)}.

1, 1, 2, 4, 12, 33, 107, 338, 1180, 4076, 14842, 54278, 204905, 779173, 3021664, 11825850, 46902050, 187562192, 757472538, 3082083587, 12636064926, 52138079196, 216474788462, 903754670864, 3792652541984, 15991642279661, 67729511771824, 288033488468257, 1229636546184773, 5268303831391151

Offset

0,3

Links

Table of n, a(n) for n=0..29.

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, 1 + k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[i, 1 + j, -1 + k, -1 + n] + aux[1 + i, j, 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: A005028 A231356 A148196 * A148198 A148199 A343663

Adjacent sequences: A148194 A148195 A148196 * A148198 A148199 A148200

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved