%I A148459
%S A148459 1,1,2,6,18,57,198,709,2601,9864,38148,149808,598372,2419970,9889001,40838480,
               170083988,
%T A148459 713613807,3015878875,12823991428,54829658278,235678930783,1017743418774,
               4413589486399,
%U A148459 19218488856579,83989136588578,368284554761549,1620125911384969,7147971908460116
%N A148459 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, 0), 
               (0, -1, 1), (0, 0, 1), (1, 1, -1)}
%H A148459 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 A148459 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[i, 
               j, -1 + k, -1 + n] + aux[i, 1 + j, -1 + k, -1 + n] + aux[1 + i, j, 
               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 A148459 Sequence in context: A000957 A125305 A148458 this_sequence A081057 A000137 
               A151282
%Y A148459 Adjacent sequences: A148456 A148457 A148458 this_sequence A148460 A148461 
               A148462
%K A148459 nonn,walk
%O A148459 0,3
%A A148459 Manuel Kauers (manuel(AT)kauers.de), Nov 18 2008