A151229 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, 0, 0), (0, -1, 0), (0, 0, 1), (1, 1, 0), (1, 1, 1)}.

1, 3, 13, 59, 273, 1291, 6189, 29891, 145249, 709331, 3476493, 17086667, 84178545, 415508571, 2054190637, 10169032019, 50397605313, 250010003619, 1241263435021, 6167119171419, 30659990460625, 152510262852267, 758988477453101, 3778818907367395, 18820920951738145, 93771668361349491

Offset

0,2

Links

Table of n, a(n) for n=0..25.

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[i, j, -1 + k, -1 + n] + aux[i, 1 + j, k, -1 + n] + aux[1 + i, 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: A052984 A360143 A262664 * A333472 A151230 A151231

Adjacent sequences: A151226 A151227 A151228 * A151230 A151231 A151232

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved