A149016 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, 1), (0, -1, 1), (0, 1, 1), (1, 1, -1)}.

1, 1, 3, 9, 35, 124, 505, 1986, 8332, 34590, 148477, 636316, 2779009, 12157264, 53805721, 238768325, 1067794767, 4788480698, 21592411576, 97615331419, 443124695004, 2016183557312, 9202926348780, 42092256924557, 193015496297659, 886662045847162, 4081658522126465, 18819149960554654

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, 1 + k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[i, 1 + j, -1 + k, -1 + n] + aux[1 + i, j, -1 + 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: A149014 A149015 A151452 * A149017 A149018 A149019

Adjacent sequences: A149013 A149014 A149015 * A149017 A149018 A149019

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved