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%I A151079 #4 Apr 21 2024 22:21:42
%S A151079 1,3,10,41,168,727,3219,14385,65613,300679,1392830,6492134,30415783,
%T A151079 143309584,677504561,3216099178,15311310131,73103177454,349911386579,
%U A151079 1678491213789,8068384917616,38852770111657,187412268123453,905363554615997,4379869444310765,21215628878755604,102888394500800977
%N A151079 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), (0, 1, 1), (1, 0, 0), (1, 0, 1)}.
%H A151079 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 A151079 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, -1 + k, -1 + n] + aux[-1 + i, j, k, -1 + n] + aux[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 A151079 nonn,walk
%O A151079 0,2
%A A151079 _Manuel Kauers_, Nov 18 2008

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