OFFSET
0,2
LINKS
Robert Israel, Table of n, a(n) for n = 0..400
A. Bostan and M. Kauers, Automatic Classification of Restricted Lattice Walks, arXiv:0811.2899 [math.CO], 2008-2009.
M. Bousquet-Mélou and M. Mishna, Walks with small steps in the quarter plane, arXiv:0810.4387 [math.CO], 2008-2009.
MAPLE
F:= proc(x, y, n) option remember; local t, s, u;
t:= 0:
if n <= min(x, y) then return 6^n fi;
for s in [[-1, 1], [-1, 0], [0, 1], [1, -1], [1, 0], [1, 1]] do
u:= [x, y]+s;
if min(u) >= 0 then t:= t + procname(op(u), n-1) fi
od;
t
end proc:
seq(F(0, 0, n), n=0..40); # Robert Israel, Jun 05 2018
MATHEMATICA
aux[i_Integer, j_Integer, n_Integer] := Which[Min[i, j, n] < 0 || Max[i, j] > n, 0, n == 0, KroneckerDelta[i, j, n], True, aux[i, j, n] = aux[-1 + i, -1 + j, -1 + n] + aux[-1 + i, j, -1 + n] + aux[-1 + i, 1 + j, -1 + n] + aux[i, -1 + j, -1 + n] + aux[1 + i, -1 + j, -1 + n] + aux[1 + i, j, -1 + n]]; Table[Sum[aux[i, j, n], {i, 0, n}, {j, 0, n}], {n, 0, 25}]
CROSSREFS
KEYWORD
nonn,walk
AUTHOR
Manuel Kauers, Nov 18 2008
STATUS
approved