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A213114 Number of binary arrays of length n+7 with fewer than 4 ones in any length 8 subsequence (=less than 50% duty cycle) 1

%I #5 Jun 05 2012 22:22:51

%S 93,151,252,424,714,1198,1996,3292,5359,8758,14401,23772,39313,65046,

%T 107572,177700,293113,483115,796360,1313385,2167141,3576909,5904270,

%U 9745234,16082476,26536889,43783532,72238736,119193082,196678607

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

%C Column 4 of A213118

%H R. H. Hardin, <a href="/A213114/b213114.txt">Table of n, a(n) for n = 1..210</a>

%F 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 Some solutions for n=3

%e ..1....0....1....0....1....1....1....1....0....1....1....1....0....0....0....0

%e ..0....0....0....1....1....0....1....1....1....0....1....0....0....1....0....0

%e ..0....1....0....0....0....1....1....0....0....0....0....0....1....1....0....1

%e ..1....0....0....0....1....0....0....1....0....0....0....0....0....0....0....0

%e ..0....0....0....0....0....0....0....0....1....1....0....0....0....1....0....1

%e ..0....1....1....0....0....0....0....0....1....0....0....0....0....0....0....1

%e ..0....0....0....0....0....1....0....0....0....0....1....0....1....0....1....0

%e ..0....0....1....0....0....0....0....0....0....1....0....0....0....0....1....0

%e ..1....0....0....0....1....0....0....1....0....0....0....1....0....0....0....0

%e ..1....1....1....0....0....1....1....1....1....0....1....0....1....0....0....0

%K nonn

%O 1,1

%A _R. H. Hardin_ Jun 05 2012

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