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%I A150463 #4 Dec 29 2023 00:12:48
%S A150463 1,2,7,25,97,398,1679,7288,32223,144618,657031,3014433,13946921,
%T A150463 64978210,304552559,1434806969,6790079675,32260223432,153804362391,
%U A150463 735548808541,3527375302589,16957713624004,81705722271403,394471543356170,1907993817660033,9244134602541970,44856136835227851,217966184541636587
%N A150463 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, 1), (0, 0, 1), (0, 1, -1), (1, 0, -1), (1, 1, 0)}.
%H A150463 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 A150463 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, k, -1 + n] + aux[-1 + i, j, 1 + k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[1 + i, 1 + j, -1 + k, -1 + n]]; Table[Sum[aux[i, j, k, n], {i, 0, n}, {j, 0, n}, {k, 0, n}], {n, 0, 10}]
%K A150463 nonn,walk
%O A150463 0,2
%A A150463 _Manuel Kauers_, Nov 18 2008

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