%I A149759
%S A149759 1,1,5,19,71,287,1211,5209,22433,97741,431877,1921997,8605981,38690161,
               174755445,793122851,
%T A149759 3611837535,16499831447,75559798515,346876213967,1596359816971,7361342844775,
               34008838169115,
%U A149759 157366474726651,729297458819767,3384981878898179,15731819597690843,73204456226077479
%N A149759 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, 0, -1), (1, 1, 1)}
%H A149759 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 A149759 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[-1 
               + i, 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}]
%Y A149759 Sequence in context: A001834 A099393 A083588 this_sequence A149760 A149761 
               A149762
%Y A149759 Adjacent sequences: A149756 A149757 A149758 this_sequence A149760 A149761 
               A149762
%K A149759 nonn,walk
%O A149759 0,3
%A A149759 Manuel Kauers (manuel(AT)kauers.de), Nov 18 2008