A150747 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, 1, 1), (0, 0, -1), (1, 0, 1), (1, 1, 0)}.

1, 2, 8, 29, 126, 537, 2425, 10961, 50711, 235665, 1107734, 5232216, 24871809, 118726407, 569049504, 2736451496, 13196496626, 63803454991, 309138528256, 1500831550268, 7298596720638, 35549469936136, 173388821932599, 846758809565578, 4139917910331022, 20261613086661582, 99259150135499873

Offset

0,2

Links

Table of n, a(n) for n=0..26.

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, -1 + k, -1 + n] + aux[i, j, 1 + k, -1 + n] + aux[1 + i, -1 + j, -1 + 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: A150744 A150745 A150746 * A150748 A150749 A150750

Adjacent sequences: A150744 A150745 A150746 * A150748 A150749 A150750

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved