A148732 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, 1), (1, 0, -1), (1, 0, 1)}.

1, 1, 3, 7, 25, 74, 267, 847, 3167, 10712, 40257, 139604, 532924, 1900636, 7273193, 26251803, 101343481, 371507374, 1436174137, 5301489284, 20609292066, 76827784934, 298927689513, 1119402842340, 4372297422984, 16484325554864, 64425113598170, 243667215669166, 955006117274724, 3629952812053204

Offset

0,3

Links

Table of n, a(n) for n=0..29.

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, j, -1 + k, -1 + n] + aux[-1 + i, j, 1 + k, -1 + n] + aux[1 + i, -1 + 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: A143339 A148730 A148731 * A151269 A130463 A148733

Adjacent sequences: A148729 A148730 A148731 * A148733 A148734 A148735

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved