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%I #8 Dec 18 2018 09:24:53
%S 1,2,3,4,5,5,6,7,8,8,9,9,10,11,12,12,13,13,14,15,16,16,17,18,19,20,21,
%T 21,22,22,23,24,25,26,27,27,28,29,30,30,31,31,32,33,34,34,35,35,36,37,
%U 38,38,39,40,41,42,43,43,44,44,45,46,47,48,49,49,50,51,52,52,53,53,54,55,56,56
%N Number of length 1 1..(n+1) arrays with every leading partial sum divisible by 2, 3 or 5.
%H R. H. Hardin, <a href="/A254828/b254828.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = a(n-1) + a(n-30) - a(n-31).
%F Empirical g.f.: x*(1 + x + x^2 + x^3 + x^4 + x^6 + x^7 + x^8 + x^10 + x^12 + x^13 + x^14 + x^16 + x^18 + x^19 + x^20 + x^22 + x^23 + x^24 + x^25 + x^26 + x^28) / ((1 - x)^2*(1 + x)*(1 - x + x^2)*(1 + x + x^2)*(1 - x + x^2 - x^3 + x^4)*(1 + x + x^2 + x^3 + x^4)*(1 - x + x^3 - x^4 + x^5 - x^7 + x^8)*(1 + x - x^3 - x^4 - x^5 + x^7 + x^8)). - _Colin Barker_, Dec 18 2018
%e All solutions for n=4:
%e ..2....5....3....4
%Y Row 1 of A254827.
%K nonn
%O 1,2
%A _R. H. Hardin_, Feb 08 2015
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