A149179 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, 0), (1, 0, -1), (1, 1, 0)}.

1, 1, 4, 10, 36, 118, 452, 1616, 6452, 24568, 100709, 398422, 1666159, 6782906, 28786448, 119623684, 513732828, 2169837355, 9406969512, 40239469006, 175836286213, 760059422197, 3343274745400, 14575762567303, 64479991320354, 283163153095060, 1258803828287115, 5562133587889050

Offset

0,3

Links

Table of n, a(n) for n=0..27.

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[-1 + i, 1 + j, 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: A359688 A358212 A088013 * A149180 A149181 A149182

Adjacent sequences: A149176 A149177 A149178 * A149180 A149181 A149182

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved