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%I A150293 #4 Jan 16 2022 00:25:55
%S A150293 1,2,6,23,94,391,1674,7340,32810,148460,677221,3113945,14427443,
%T A150293 67248566,314944257,1480937061,6990005401,33106706997,157268520653,
%U A150293 748999807143,3575464723018,17104963318797,81991933706087,393724722012390,1893722027888591,9122010044437447,44001916585556279,212527283465755898
%N A150293 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, 0), (0, 1, 0), (1, 0, 1), (1, 1, -1)}.
%H A150293 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 A150293 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, j, -1 + k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[1 + i, -1 + 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}]
%K A150293 nonn,walk
%O A150293 0,2
%A A150293 _Manuel Kauers_, Nov 18 2008

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