A149854 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, -1, 1), (0, 1, 0), (1, 1, 0)}.

1, 2, 5, 13, 37, 111, 346, 1100, 3557, 11683, 38926, 131154, 445765, 1526305, 5261985, 18254431, 63672445, 223138635, 785267758, 2774187398, 9835528373, 34983477901, 124795716145, 446376963933, 1600610895841, 5752771831361, 20720666878796, 74782199279800, 270397125942817, 979410568546113, 3553373294757136

Offset

0,2

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, -1 + j, k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[1 + i, 1 + 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: A193114 A114509 A003080 * A151442 A263529 A053732

Adjacent sequences: A149851 A149852 A149853 * A149855 A149856 A149857

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved