%I #5 May 17 2012 14:27:37
%S 150,486,1597,5211,16649,53553,172980,558743,1801720,5808944,18737526,
%T 60447764,194984049,628912080,2028584905,6543438398,21106550023,
%U 68080857417,219600230083,708339701336,2284812500323,7369860423165
%N Number of 0..3 arrays of length n+3 with sum no more than 6 in any length 4 subsequence (=50% duty cycle)
%C Column 2 of A212471
%H R. H. Hardin, <a href="/A212465/b212465.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 2*a(n-1) +3*a(n-2) +17*a(n-4) -8*a(n-5) -42*a(n-6) -8*a(n-7) -59*a(n-8) +26*a(n-9) +147*a(n-10) +33*a(n-11) +112*a(n-12) -115*a(n-13) -293*a(n-14) -5*a(n-15) -93*a(n-16) +221*a(n-17) +370*a(n-18) -65*a(n-19) +3*a(n-20) -242*a(n-21) -279*a(n-22) +78*a(n-23) +21*a(n-24) +176*a(n-25) +184*a(n-26) -33*a(n-27) -15*a(n-28) -87*a(n-29) -132*a(n-30) -7*a(n-31) +36*a(n-32) +35*a(n-33) +69*a(n-34) +5*a(n-35) -30*a(n-36) -10*a(n-37) -20*a(n-38) +10*a(n-40) +a(n-41) +2*a(n-42) -a(n-44)
%e Some solutions for n=3
%e ..3....0....1....1....0....0....0....1....1....0....0....3....0....0....2....1
%e ..1....3....1....0....3....2....0....3....2....2....3....1....0....3....0....1
%e ..1....1....1....2....0....0....0....1....0....2....0....0....0....0....0....0
%e ..1....0....2....1....0....0....0....0....1....0....2....2....2....1....2....3
%e ..0....2....1....1....3....3....3....2....0....2....0....1....1....0....2....1
%e ..2....2....2....1....0....2....0....3....2....2....2....1....2....2....2....2
%K nonn
%O 1,1
%A _R. H. Hardin_ May 17 2012