%I A150565
%S A150565 1,2,7,26,107,455,1997,8960,40802,188190,876126,4110613,19409604,92128043,
               439257473,2102256709,
%T A150565 10094370187,48608230113,234652253431,1135270546210,5503323842213,26724710156090,
%U A150565 129982634911257,633105351011227,3087646339418001,15076130618030798,73691824779803129
%N A150565 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, 1), (0, -1, 1), 
               (0, 1, -1), (0, 1, 0), (1, 1, 0)}
%H A150565 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 A150565 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[i, -1 
               + j, 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]]; Table[Sum[aux[i, j, 
               k, n], {i, 0, n}, {j, 0, n}, {k, 0, n}], {n, 0, 10}]
%Y A150565 Sequence in context: A150562 A150563 A150564 this_sequence A150566 A150567 
               A000151
%Y A150565 Adjacent sequences: A150562 A150563 A150564 this_sequence A150566 A150567 
               A150568
%K A150565 nonn,walk
%O A150565 0,2
%A A150565 Manuel Kauers (manuel(AT)kauers.de), Nov 18 2008