%I A148872
%S A148872 1,1,3,8,29,95,371,1391,5579,22515,93172,389984,1660907,7129259,30986277,
               135626950,598601472,
%T A148872 2659537838,11888774528,53438424419,241407630975,1095407211522,4991553340467,
               22831078844323,
%U A148872 104797432694290,482588831392966,2228958459777283,10323814710499352,47940936376648040
%N A148872 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, -1), (1, 1, -1)}
%H A148872 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 A148872 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, 1 + j, 1 + 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 A148872 Sequence in context: A148869 A148870 A148871 this_sequence A148873 A148874 
               A022017
%Y A148872 Adjacent sequences: A148869 A148870 A148871 this_sequence A148873 A148874 
               A148875
%K A148872 nonn,walk
%O A148872 0,3
%A A148872 Manuel Kauers (manuel(AT)kauers.de), Nov 18 2008