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T(n,k)=Number of binary arrays of length n+2*k-1 with no more than k ones in any length 2k subsequence (=50% duty cycle)
11

%I #4 May 14 2012 22:08:06

%S 3,11,5,42,19,8,163,74,33,13,638,291,132,57,21,2510,1150,527,236,97,

%T 34,9908,4558,2104,959,421,166,55,39203,18100,8402,3872,1747,747,285,

%U 89,155382,71971,33560,15586,7143,3179,1314,489,144,616666,286454,134075

%N T(n,k)=Number of binary arrays of length n+2*k-1 with no more than k ones in any length 2k subsequence (=50% duty cycle)

%C Table starts

%C ..3..11...42...163...638...2510...9908...39203...155382...616666...2449868

%C ..5..19...74...291..1150...4558..18100...71971...286454..1140954...4547020

%C ..8..33..132...527..2104...8402..33560..134075...535728..2140910...8556568

%C .13..57..236...959..3872..15586..62632..251419..1008536..4043582..16206152

%C .21..97..421..1747..7143..29002.117290..473171..1905675..7665886..30810054

%C .34.166..747..3179.13185..54042.220054..892387..3609005.14567294..58714842

%C .55.285.1314..5769.24322.100736.413220.1685039..6844362.27724036.112072540

%C .89.489.2318.10425.44794.187696.776116.3183631.12990818.52815156.214150732

%H R. H. Hardin, <a href="/A212402/b212402.txt">Table of n, a(n) for n = 1..4360</a>

%e Some solutions for n=3 k=4

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

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

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

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

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

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

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

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

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

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

%Y Column 1 is A000045(n+3)

%Y Column 2 is A118647(n+3)

%Y Column 3 is A133551(n+5)

%Y Row 1 is A032443

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_ May 14 2012