A150929 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), (1, -1, 1), (1, 1, 0), (1, 1, 1)}.

1, 2, 9, 33, 151, 647, 3018, 13621, 64552, 298946, 1431184, 6738665, 32483079, 154660161, 749317281, 3595474040, 17487549016, 84392829233, 411708177842, 1995673901046, 9759296357079, 47472714974110, 232609391503454, 1134706393175152, 5569016942526946, 27229877976182930, 133826608859968609

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, -1 + k, -1 + n] + aux[-1 + i, -1 + j, k, -1 + n] + aux[-1 + 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: A150926 A150927 A150928 * A150930 A150931 A150932

Adjacent sequences: A150926 A150927 A150928 * A150930 A150931 A150932

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved