A254820 - OEIS

%I #9 Dec 18 2018 09:24:46

%S 1,2,4,5,6,9,10,11,15,19,21,26,35,48,75,120,166,203,262,395,613,879,

%T 1174,1502,1849,2237,2738,3364,4104,5107,6727,9500,14046,20588,28704,

%U 38517,52473,74917,109037,154672,209449,271287,340040,418493,512101,627661

%N Number of length n 1..(1+1) arrays with every leading partial sum divisible by 2, 3 or 5.

%H R. H. Hardin, <a href="/A254820/b254820.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = a(n-15) + 9*a(n-16) + 32*a(n-17) + 58*a(n-18) + 58*a(n-19) + 32*a(n-20) + 9*a(n-21) + a(n-22).

%F Empirical g.f.: x*(1 + x)*(1 + x + 3*x^2 + 2*x^3 + 4*x^4 + 5*x^5 + 5*x^6 + 6*x^7 + 9*x^8 + 10*x^9 + 11*x^10 + 15*x^11 + 20*x^12 + 28*x^13 + 47*x^14 + 72*x^15 + 83*x^16 + 66*x^17 + 33*x^18 + 9*x^19 + x^20) / (1 - x^15 - 9*x^16 - 32*x^17 - 58*x^18 - 58*x^19 - 32*x^20 - 9*x^21 - x^22). - _Colin Barker_, Dec 18 2018

%e All solutions for n=4:

%e ..2....2....2....2....2

%e ..1....1....2....1....2

%e ..2....1....1....1....2

%e ..1....2....1....1....2

%Y Column 1 of A254827.

%K nonn

%O 1,2

%A _R. H. Hardin_, Feb 08 2015