A149162 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, -1, 0), (-1, 1, 0), (1, -1, 1), (1, 1, 0)}

1, 1, 4, 9, 40, 115, 531, 1707, 8052, 27731, 132499, 477673, 2302126, 8577767, 41595124, 158897465, 774062896, 3015427933, 14741580123, 58341229353, 286014447954, 1146780800713, 5634802519830, 22841726382467, 112445000837320, 460097279439935, 2268513209796467, 9357465570461563, 46198374453679774

Offset

0,3

Links

Table of n, a(n) for n=0..28.

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, 1 + j, -1 + k, -1 + n] + aux[1 + i, -1 + j, k, -1 + n] + aux[1 + i, 1 + 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: A149159 A149160 A149161 * A149163 A149164 A238420

Adjacent sequences: A149159 A149160 A149161 * A149163 A149164 A149165

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved