cp's OEIS Frontend

A213114 Number of binary arrays of length n+7 with fewer than 4 ones in any length 8 subsequence (=less than 50% duty cycle).

%I A213114 #7 Jun 02 2025 08:00:26
%S A213114 93,151,252,424,714,1198,1996,3292,5359,8758,14401,23772,39313,65046,
%T A213114 107572,177700,293113,483115,796360,1313385,2167141,3576909,5904270,
%U A213114 9745234,16082476,26536889,43783532,72238736,119193082,196678607
%N A213114 Number of binary arrays of length n+7 with fewer than 4 ones in any length 8 subsequence (=less than 50% duty cycle).
%C A213114 Column 4 of A213118
%H A213114 R. H. Hardin, <a href="/A213114/b213114.txt">Table of n, a(n) for n = 1..210</a>
%F A213114 Empirical: a(n) = a(n-1) +a(n-3) +a(n-6) +a(n-7) +7*a(n-8) +a(n-9) -6*a(n-11) -3*a(n-12) -a(n-13) -5*a(n-14) -a(n-15) -21*a(n-16) -13*a(n-17) -5*a(n-18) +14*a(n-19) +9*a(n-20) -a(n-21) +10*a(n-22) +35*a(n-24) +22*a(n-25) +5*a(n-26) -20*a(n-27) -9*a(n-28) -a(n-29) -10*a(n-30) -a(n-31) -35*a(n-32) -13*a(n-33) +15*a(n-35) +3*a(n-36) +5*a(n-38) +a(n-39) +21*a(n-40) +a(n-41) -6*a(n-43) -a(n-46) -7*a(n-48) +a(n-49) +a(n-51) +a(n-56)
%e A213114 Some solutions for n=3
%e A213114 ..1....0....1....0....1....1....1....1....0....1....1....1....0....0....0....0
%e A213114 ..0....0....0....1....1....0....1....1....1....0....1....0....0....1....0....0
%e A213114 ..0....1....0....0....0....1....1....0....0....0....0....0....1....1....0....1
%e A213114 ..1....0....0....0....1....0....0....1....0....0....0....0....0....0....0....0
%e A213114 ..0....0....0....0....0....0....0....0....1....1....0....0....0....1....0....1
%e A213114 ..0....1....1....0....0....0....0....0....1....0....0....0....0....0....0....1
%e A213114 ..0....0....0....0....0....1....0....0....0....0....1....0....1....0....1....0
%e A213114 ..0....0....1....0....0....0....0....0....0....1....0....0....0....0....1....0
%e A213114 ..1....0....0....0....1....0....0....1....0....0....0....1....0....0....0....0
%e A213114 ..1....1....1....0....0....1....1....1....1....0....1....0....1....0....0....0
%K A213114 nonn
%O A213114 1,1
%A A213114 _R. H. Hardin_ Jun 05 2012