%I #4 Feb 08 2015 10:25:44

%S 4,16,54,166,500,1557,5316,19292,69536,248613,893091,3146780,10584619,

%T 34064054,108011322,350399707,1186298040,4158109604,14813200901,

%U 52859389574,186599450347,643953634665,2160180481888,7086155229600

%N Number of length n 1..(4+1) arrays with every leading partial sum divisible by 2, 3 or 5

%C Column 4 of A254827

%H R. H. Hardin, <a href="/A254823/b254823.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 3*a(n-1) -6*a(n-2) +10*a(n-3) -15*a(n-4) +21*a(n-5) -27*a(n-6) +150*a(n-7) +1910*a(n-8) +10081*a(n-9) +23355*a(n-10) +32804*a(n-11) +30881*a(n-12) +20836*a(n-13) +10122*a(n-14) +3593*a(n-15) +939*a(n-16) +180*a(n-17) +21*a(n-18) +a(n-19)

%e Some solutions for n=4

%e ..5....4....5....4....3....3....2....4....2....5....3....2....3....4....2....4

%e ..5....2....4....5....2....1....4....1....2....4....1....4....5....1....4....4

%e ..2....3....1....5....1....5....2....1....4....5....2....3....2....1....2....1

%e ..4....3....4....1....4....5....2....4....1....4....3....1....5....3....4....5

%K nonn

%O 1,1

%A _R. H. Hardin_, Feb 08 2015