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%I #8 Dec 20 2018 16:10:14
%S 1,2,3,3,4,4,5,6,7,7,8,8,9,10,11,11,12,12,13,14,15,15,16,16,17,18,19,
%T 19,20,20,21,22,23,23,24,24,25,26,27,27,28,28,29,30,31,31,32,32,33,34,
%U 35,35,36,36,37,38,39,39,40,40,41,42,43,43,44,44,45,46,47,47,48,48,49,50,51,51
%N Number of length 1 1..(n+1) arrays with every leading partial sum divisible by 2 or 3.
%H R. H. Hardin, <a href="/A257063/b257063.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = a(n-1) + a(n-6) - a(n-7).
%F Empirical for n mod 6 = 0: a(n) = (2/3)*n
%F Empirical for n mod 6 = 1: a(n) = (2/3)*n + (1/3)
%F Empirical for n mod 6 = 2: a(n) = (2/3)*n + (2/3)
%F Empirical for n mod 6 = 3: a(n) = (2/3)*n + 1
%F Empirical for n mod 6 = 4: a(n) = (2/3)*n + (1/3)
%F Empirical for n mod 6 = 5: a(n) = (2/3)*n + (2/3).
%F Empirical g.f.: x*(1 + x + x^2 + x^4) / ((1 - x)^2*(1 + x)*(1 - x + x^2)*(1 + x + x^2)). - _Colin Barker_, Dec 20 2018
%e All solutions for n=4:
%e ..2....4....3
%Y Row 1 of A257062.
%K nonn
%O 1,2
%A _R. H. Hardin_, Apr 15 2015
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