%I #4 Dec 02 2014 09:01:51
%S 1,1,4,13,42,146,520,1893,6928,25520,95258,357332,1348314,5109674,
%T 19419422,74124571,283750244,1089053340,4189218564,16143369610,
%U 62342218516,241154261642,934254937426,3624326380994,14076738707662,54742699821140,213116870712502,830503102890218,3239368922556944
%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, 0, 0), (0, 1, 0), (0, 1, 1), (1, 1, 1)}.
%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, 1 + k, 1 + n] + aux[i, 1 + j, 1 + k, 1 + n] + aux[i, 1 + j, k, 1 + n] + aux[1 + i, 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 0,3
%A _Manuel Kauers_, Nov 18 2008
