A150030 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, 0, 0), (1, 0, 1)}.

1, 2, 6, 16, 62, 209, 826, 2884, 12299, 46495, 197275, 752364, 3328340, 13257631, 58135717, 231929737, 1046257805, 4296230064, 19202622824, 78758167294, 359644608451, 1506796125323, 6819578915478, 28503632171786, 131253674953941, 557875859380520, 2547299431112866, 10794901911340637

Offset

0,2

Links

Robert Israel, Table of n, a(n) for n = 0..225

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

Maple

F:= proc(x, y, z, n) option remember; local t, s, u;
     t:= 0:
     if n <= min(x, y, z) then return 5^n fi;
     for s in [[-1, -1, -1], [-1, -1, 0], [-1, 1, 0], [1, 0, 0], [1, 0, 1]] do
       u:= [x, y, z]+s;
       if min(u) >= 0 then t:= t + procname(op(u), n-1) fi
     od;
     t
end proc:
seq(F(0, 0, 0, n), n=0..40); # Robert Israel, Jun 28 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, j, -1 + k, -1 + n] + aux[-1 + i, j, 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: A033301 A197102 A093113 * A150031 A121753 A173994

Adjacent sequences: A150027 A150028 A150029 * A150031 A150032 A150033

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved