0,2

Robert Israel, Table of n, a(n) for n = 0..800

A. Bostan and Manuel Kauers, Automatic Classification of Restricted Lattice Walks, arXiv:0811.2899 [math.CO], 2008.

M. Bousquet-Mélou and M. Mishna, Walks with small steps in the quarter plane, arXiv:0810.4387 [math.CO], 2008.

steps:= [[-1, -1], [-1, 1], [1, 0], [1, 1]]:

f:= proc(n, p) option remember; local t;

if n <= min(p) then return 4^n fi;

add(procname(n-1, t), t=remove(has, map(`+`, steps, p), -1));

end proc:

map(f, [$0..100], [0, 0]); # Robert Israel, Nov 09 2025

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[1 + i, 1 + j, -1 + n]]; Table[Sum[aux[i, j, n], {i, 0, n}, {j, 0, n}], {n, 0, 25}]

Sequence in context: A319852 A060900 A305850 * A150300 A150301 A150302

Adjacent sequences: A151286 A151287 A151288 * A151290 A151291 A151292

nonn,walk

Manuel Kauers, Nov 18 2008

approved