A148697 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), (0, 1, -1), (0, 1, 1), (1, 0, -1)}.

1, 1, 3, 7, 23, 68, 238, 808, 2938, 10648, 40124, 151756, 588055, 2291058, 9060331, 36091349, 145241654, 588352708, 2401710933, 9859511586, 40725262278, 169064929135, 705330976327, 2955456026216, 12435560347258, 52522752590770, 222636983923895, 946849375091588, 4039450962870771

Offset

0,3

Links

Table of n, a(n) for n=0..28.

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, -1 + j, -1 + k, -1 + n] + aux[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: A148694 A148695 A148696 * A148698 A148699 A181999

Adjacent sequences: A148694 A148695 A148696 * A148698 A148699 A148700

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved