%I A149031
%S A149031 1,1,3,10,33,127,486,1943,8052,33504,143203,618615,2696818,11919409,52965105,
               237386849,
%T A149031 1071312485,4857376568,22160738643,101518175550,467022106982,2157328576831,
               9996509638302,
%U A149031 46480743976377,216739174880976,1013326106030851,4750067786683020,22315803215975305
%N A149031 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), (-1, 1, 0), 
               (0, 1, -1), (1, -1, 0), (1, 0, 1)}
%H A149031 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 A149031 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, j, -1 + k, -1 + n] + aux[-1 + 
               i, 1 + j, k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[1 + i, 
               -1 + j, 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}]
%Y A149031 Sequence in context: A111639 A149029 A149030 this_sequence A145928 A006535 
               A041633
%Y A149031 Adjacent sequences: A149028 A149029 A149030 this_sequence A149032 A149033 
               A149034
%K A149031 nonn,walk
%O A149031 0,3
%A A149031 Manuel Kauers (manuel(AT)kauers.de), Nov 18 2008