OFFSET
0,3
LINKS
Robert Israel, Table of n, a(n) for n = 0..225
Alin Bostan and Manuel Kauers, Automatic Classification of Restricted Lattice Walks, arXiv:0811.2899 [math.CO], 2009.
MAPLE
Steps:= [[-1, -1, 0], [-1, -1, 1], [-1, 0, 1], [0, 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..30], [0, 0, 0]); # Robert Israel, Feb 27 2022
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[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, k, -1 + n]]; Table[Sum[aux[i, j, k, n], {i, 0, n}, {j, 0, n}, {k, 0, n}], {n, 0, 10}]
CROSSREFS
KEYWORD
nonn,walk
AUTHOR
Manuel Kauers, Nov 18 2008
STATUS
approved