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%I #5 Jul 09 2018 16:04:25
%S 1,1,5,13,63,201,991,3543,17589,66675,331981,1310121,6533329,26526137,
%T 132398363,548964603,2741549255,11553795573,57721223997,246430668963,
%U 1231434003299,5313224430041,26554997020499,115586008363819,577754385702581,2533497279476529,12664663772458771,55888692416822733
%N 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, 1, -1), (1, -1, 0), (1, -1, 1), (1, 1, 1)}
%H Robert Israel, <a href="/A149570/b149570.txt">Table of n, a(n) for n = 0..182</a>
%H A. Bostan and M. Kauers, 2008. Automatic Classification of Restricted Lattice Walks, <a href="http://arxiv.org/abs/0811.2899">ArXiv 0811.2899</a>.
%p Steps:= [[-1, -1, 1], [-1, 1, -1], [1, -1, 0], [1, -1, 1], [1, 1, 1]]:
%p f:= proc(n, p) option remember;
%p if n <= min(p) then return 5^n fi;
%p add(procname(n-1, t), t=remove(has, map(`+`, Steps, p), -1));
%p end proc: map(f, [$0..40], [0, 0, 0]); # _Robert Israel_, Jul 09 2018
%t 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, 1 + j, -1 + k, -1 + n] + aux[-1 + i, 1 + j, k, -1 + n] + aux[1 + i, -1 + 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 nonn,walk
%O 0,3
%A _Manuel Kauers_, Nov 18 2008
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