%I A149030
%S A149030 1,1,3,10,33,124,478,1876,7653,31520,131923,560361,2397177,10362660,45122797,
               197619125,
%T A149030 871134632,3857758844,17160398867,76658932408,343609269081,1545368262356,
               6971119129314,
%U A149030 31529648390000,142971072421910,649780474978174,2959380924404418,13505223883964250
%N A149030 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, 0), (-1, 0, 1), 
               (0, 1, 1), (1, -1, 0), (1, 0, -1)}
%H A149030 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 A149030 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[-1 + 
               i, 1 + j, k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[1 + i, 
               j, -1 + k, -1 + n] + aux[1 + i, 1 + j, k, -1 + n]]; Table[Sum[aux[i, 
               j, k, n], {i, 0, n}, {j, 0, n}, {k, 0, n}], {n, 0, 10}]
%Y A149030 Sequence in context: A001558 A111639 A149029 this_sequence A149031 A145928 
               A006535
%Y A149030 Adjacent sequences: A149027 A149028 A149029 this_sequence A149031 A149032 
               A149033
%K A149030 nonn,walk
%O A149030 0,3
%A A149030 Manuel Kauers (manuel(AT)kauers.de), Nov 18 2008