A148850 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, 0), (1, 0, 1), (1, 1, -1)}.

1, 1, 3, 8, 28, 91, 339, 1191, 4673, 17489, 70829, 275583, 1140249, 4555059, 19176287, 78180708, 333655636, 1382789189, 5964790733, 25047746365, 108998800785, 462656900979, 2028379249377, 8687945066980, 38332181892050, 165464671038519, 734031617783073, 3189844310837718, 14217991701913836

Offset

0,3

Links

Robert Israel, Table of n, a(n) for n = 0..220

A. Bostan and M. Kauers, 2008. Automatic Classification of Restricted Lattice Walks, ArXiv 0811.2899.

Maple

Steps:= [[-1, -1, -1], [-1, -1, 1], [-1, 0, 0], [1, 0, 1], [1, 1, -1]]:
f:= proc(n, p) option remember;
 if n <= min(p) then return 5^n fi;
   add(procname(n-1, t), t=remove(has, map(`+`, Steps, p), -1));
end proc:
map(f, [$0..40], [0, 0, 0]); # Robert Israel, May 02 2018

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[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: A148847 A148848 A148849 * A148851 A148852 A148853

Adjacent sequences: A148847 A148848 A148849 * A148851 A148852 A148853

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved