cp's OEIS Frontend

A212398 Number of binary arrays of length n+7 with no more than 4 ones in any length 8 subsequence (=50% duty cycle).

%I A212398 #7 Jun 02 2025 07:56:38
%S A212398 163,291,527,959,1747,3179,5769,10425,18729,33706,60797,109800,198415,
%T A212398 358592,647959,1170415,2113372,3815438,6888722,12439093,22463681,
%U A212398 40568913,73266801,132315810,238948339,431506179,779231793,1407175435
%N A212398 Number of binary arrays of length n+7 with no more than 4 ones in any length 8 subsequence (=50% duty cycle).
%C A212398 Column 4 of A212402
%H A212398 R. H. Hardin, <a href="/A212398/b212398.txt">Table of n, a(n) for n = 1..210</a>
%F A212398 Empirical: a(n) = a(n-1) +a(n-2) +a(n-4) -a(n-6) +3*a(n-7) +8*a(n-8) -8*a(n-10) -8*a(n-11) -10*a(n-12) -5*a(n-13) +8*a(n-14) -2*a(n-15) -28*a(n-16) -15*a(n-17) +25*a(n-18) +24*a(n-19) +28*a(n-20) +24*a(n-21) -19*a(n-22) -18*a(n-23) +51*a(n-24) +40*a(n-25) -55*a(n-26) -16*a(n-27) -55*a(n-28) -45*a(n-29) +51*a(n-30) +36*a(n-31) -61*a(n-32) -45*a(n-33) +70*a(n-34) -16*a(n-35) +67*a(n-36) +40*a(n-37) -70*a(n-38) -19*a(n-39) +56*a(n-40) +24*a(n-41) -58*a(n-42) +24*a(n-43) -56*a(n-44) -15*a(n-45) +56*a(n-46) -2*a(n-47) -28*a(n-48) -5*a(n-49) +28*a(n-50) -8*a(n-51) +28*a(n-52) -28*a(n-54) +3*a(n-55) +8*a(n-56) -8*a(n-58) -8*a(n-60) +a(n-61) +8*a(n-62) -a(n-64) +a(n-66) +a(n-68) -a(n-70)
%e A212398 Some solutions for n=3
%e A212398 ..0....0....1....0....0....0....1....0....0....0....1....1....0....1....1....0
%e A212398 ..1....0....0....0....0....0....0....0....0....1....0....0....0....1....0....0
%e A212398 ..1....0....1....0....1....1....0....0....0....1....1....1....0....0....0....0
%e A212398 ..0....1....0....1....0....0....0....0....0....0....0....0....0....1....0....0
%e A212398 ..0....0....0....0....0....1....1....1....0....1....1....1....0....0....0....0
%e A212398 ..0....0....1....0....1....0....1....0....1....0....0....0....0....0....1....1
%e A212398 ..0....1....1....1....1....0....0....0....1....1....0....1....0....1....0....0
%e A212398 ..0....0....0....0....0....0....0....1....1....0....1....0....0....0....1....0
%e A212398 ..1....1....0....0....0....1....1....0....0....0....1....0....0....1....1....1
%e A212398 ..0....0....1....0....0....1....1....0....1....1....0....1....0....1....1....1
%K A212398 nonn
%O A212398 1,1
%A A212398 _R. H. Hardin_ May 14 2012