%I A148997
%S A148997 1,1,3,9,33,121,468,1859,7558,31270,131330,558115,2396603,10379648,45292679,
               198926208,
%T A148997 878692550,3900981744,17396764823,77896353911,350065380105,1578398595372,
               7138256186788,
%U A148997 32371596240950,147175354377729,670685606484390,3062947647863016,14016157023522647
%N A148997 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), (-1, 0, 1), 
               (0, 1, -1), (0, 1, 1), (1, -1, 1)}
%H A148997 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 A148997 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, 1 + k, -1 + n] + aux[1 + 
               i, j, -1 + 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}]
%Y A148997 Sequence in context: A148994 A148995 A148996 this_sequence A082841 A151038 
               A039648
%Y A148997 Adjacent sequences: A148994 A148995 A148996 this_sequence A148998 A148999 
               A149000
%K A148997 nonn,walk
%O A148997 0,3
%A A148997 Manuel Kauers (manuel(AT)kauers.de), Nov 18 2008