%I A151253
%S A151253 1,4,19,91,445,2188,10819,53644,266581,1326646,6609307,32953033,164397313,
               820521562,4096733707,
%T A151253 20459928259,102203137741,510621146326,2551485015379,12750737780587,63725988599425,
%U A151253 318514790389294,1592093707211299,7958459733327676,39783873348471745,198883941062337328
%N A151253 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, 0, 1), (1, 
               0, 0), (1, 0, 1), (1, 1, 0)}
%C A151253 Binomial transform of A151162 . [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), 
               Feb 03 2009]
%H A151253 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 A151253 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[-1 + i, j, k, -1 + n] + aux[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 A151253 Sequence in context: A010907 A087449 A004253 this_sequence A121179 A131552 
               A122369
%Y A151253 Adjacent sequences: A151250 A151251 A151252 this_sequence A151254 A151255 
               A151256
%K A151253 nonn,walk
%O A151253 0,2
%A A151253 Manuel Kauers (manuel(AT)kauers.de), Nov 18 2008