%I A148573
%S A148573 1,1,3,6,20,49,172,484,1732,5162,18965,59680,220777,715673,2685204,8953384,
               33734326,114539085,
%T A148573 435187894,1503531596,5729591256,20035479823,76771639039,271669011838,
               1043251861255,
%U A148573 3723452781558,14354596419363,51678596017672,199560683860979,723042091109072,
               2800255744221056
%N A148573 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, 1), (0, 0, -1), 
               (0, 1, -1), (1, 0, 1)}
%H A148573 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 A148573 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[i, -1 
               + j, 1 + k, -1 + n] + aux[i, j, 1 + k, -1 + n] + aux[1 + i, 1 + 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 A148573 Sequence in context: A081181 A062164 A052408 this_sequence A148574 A005558 
               A138350
%Y A148573 Adjacent sequences: A148570 A148571 A148572 this_sequence A148574 A148575 
               A148576
%K A148573 nonn,walk
%O A148573 0,3
%A A148573 Manuel Kauers (manuel(AT)kauers.de), Nov 18 2008