A151190 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), (0, 1, -1), (1, 0, 0), (1, 0, 1), (1, 1, 1)}

1, 3, 12, 52, 233, 1083, 5100, 24295, 116918, 565724, 2752468, 13446199, 65884595, 323738565, 1594128852, 7864002439, 38855552063, 192229773083, 952108277471, 4720386488466, 23422582031478, 116310271773159, 577941027197706, 2873420290878204, 14293452937971562, 71133050139234528, 354145607242254419

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, j, -1 + k, -1 + n] + aux[-1 + i, j, k, -1 + n] + aux[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: A368971 A362595 A125187 * A151191 A151192 A151193

Adjacent sequences: A151187 A151188 A151189 * A151191 A151192 A151193

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved