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%I A149973 #4 Dec 28 2023 23:13:55
%S A149973 1,2,5,16,56,204,780,3099,12594,52123,219696,939511,4061334,17733255,
%T A149973 78151761,347048149,1551225434,6976462330,31550130733,143365879422,
%U A149973 654323444492,2998603009552,13792688901614,63654344411450,294688265919191,1368229743361834,6369561861745394,29725712375089444
%N A149973 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, 1, 1), (0, 1, 0), (1, 0, -1), (1, 0, 0)}.
%H A149973 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 A149973 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, k, -1 + n] + aux[-1 + i, j, 1 + k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[1 + i, -1 + 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 A149973 nonn,walk
%O A149973 0,2
%A A149973 _Manuel Kauers_, Nov 18 2008

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