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%I #6 Oct 23 2013 18:19:09
%S 1,1,5,11,49,157,629,2319,9309,36067,146735,583717,2403149,9754979,
%T 40462171,166354683,695612827,2888616957,12146055243,50820925053,
%U 214800425487,904468489247,3837974122189,16240475548249,69171748577847,293963559264191,1255748732370767,5355420642656009
%N 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), (1, -1, -1), (1, -1, 1), (1, 1, 1)}.
%H Alois P. Heinz, <a href="/A149516/b149516.txt">Table of n, a(n) for n = 0..100</a>
%H 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 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[-1 + 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}]
%K nonn,walk
%O 0,3
%A _Manuel Kauers_, Nov 18 2008
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