A148177 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, 1, -1), (0, 0, 1), (1, 0, -1)}.

1, 1, 2, 4, 12, 28, 86, 238, 784, 2325, 8058, 25360, 90373, 297465, 1086446, 3692655, 13756875, 48012753, 181628315, 647909195, 2482768099, 9016569288, 34932498872, 128802722018, 503682591606, 1881611341779, 7417610261825, 28025251640045, 111265114651271, 424562759910862, 1696155023650389

Offset

0,3

Links

Table of n, a(n) for n=0..30.

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, j, -1 + k, -1 + n] + aux[1 + i, -1 + 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: A151258 A148175 A148176 * A080876 A148178 A148179

Adjacent sequences: A148174 A148175 A148176 * A148178 A148179 A148180

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved