%I
%S 1,3,12,52,237,1099,5213,24940,120389,584838,2853373,13976063,
%T 68652709,338034589,1667756201,8241492662,40782808665,202049395507,
%U 1002001335467,4973396367842,24703642321516,122786278471416,610640791721211,3038355979978879,15124580771488710,75317942432483327
%N 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, 0), (0, 1, 1), (0, 1, 1), (1, 0, 1), (1, 1, 0)}
%H A. Bostan and M. Kauers, 2008. Automatic Classification of Restricted Lattice Walks, <a href="http://arxiv.org/abs/0811.2899">ArXiv 0811.2899</a>.
%t 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, k, 1 + n] + aux[1 + i, j, 1 + k, 1 + n] + aux[i, 1 + j, 1 + k, 1 + n] + aux[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}]
%K nonn,walk
%O 0,2
%A _Manuel Kauers_, Nov 18 2008
