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%I A148575 #4 Mar 18 2023 23:17:46
%S A148575 1,1,3,6,20,50,181,513,1981,6087,24450,79265,326192,1098561,4604660,
%T A148575 15968636,67934917,241144724,1037831560,3753744245,16303956286,
%U A148575 59889623003,262114436704,975484574708,4296973313554,16171297126704,71624751796375,272169868078628,1211149718585558,4641314003656235
%N A148575 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), (-1, 0, 0), (-1, 0, 1), (1, 0, 0), (1, 1, -1)}.
%H A148575 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 A148575 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, k, -1 + n] + aux[1 + i, j, -1 + k, -1 + n] + aux[1 + i, j, 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 A148575 nonn,walk
%O A148575 0,3
%A A148575 _Manuel Kauers_, Nov 18 2008

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