cp's OEIS Frontend

A212402 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).

%I A212402 #6 Jun 02 2025 07:57:06
%S A212402 3,11,5,42,19,8,163,74,33,13,638,291,132,57,21,2510,1150,527,236,97,
%T A212402 34,9908,4558,2104,959,421,166,55,39203,18100,8402,3872,1747,747,285,
%U A212402 89,155382,71971,33560,15586,7143,3179,1314,489,144,616666,286454,134075
%N A212402 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 A212402 Table starts
%C A212402 ..3..11...42...163...638...2510...9908...39203...155382...616666...2449868
%C A212402 ..5..19...74...291..1150...4558..18100...71971...286454..1140954...4547020
%C A212402 ..8..33..132...527..2104...8402..33560..134075...535728..2140910...8556568
%C A212402 .13..57..236...959..3872..15586..62632..251419..1008536..4043582..16206152
%C A212402 .21..97..421..1747..7143..29002.117290..473171..1905675..7665886..30810054
%C A212402 .34.166..747..3179.13185..54042.220054..892387..3609005.14567294..58714842
%C A212402 .55.285.1314..5769.24322.100736.413220.1685039..6844362.27724036.112072540
%C A212402 .89.489.2318.10425.44794.187696.776116.3183631.12990818.52815156.214150732
%H A212402 R. H. Hardin, <a href="/A212402/b212402.txt">Table of n, a(n) for n = 1..4360</a>
%e A212402 Some solutions for n=3 k=4
%e A212402 ..0....0....0....1....0....0....0....0....1....1....1....0....1....0....1....1
%e A212402 ..1....0....1....1....0....0....1....0....1....1....0....1....1....1....0....0
%e A212402 ..1....1....1....0....1....0....1....0....1....0....1....0....0....0....0....0
%e A212402 ..0....1....1....0....1....0....1....0....0....1....0....1....1....0....1....0
%e A212402 ..1....0....0....0....1....1....1....1....0....0....1....0....0....1....0....0
%e A212402 ..0....0....0....1....0....1....0....0....0....0....0....0....0....0....1....0
%e A212402 ..0....0....0....0....0....0....0....0....0....0....0....0....0....1....1....1
%e A212402 ..0....1....1....0....0....1....0....1....0....1....1....0....1....0....0....1
%e A212402 ..0....0....0....1....0....1....0....1....1....1....1....1....0....0....0....1
%e A212402 ..1....0....0....1....1....0....0....0....1....1....0....1....0....0....1....1
%Y A212402 Column 1 is A000045(n+3)
%Y A212402 Column 2 is A118647(n+3)
%Y A212402 Column 3 is A133551(n+5)
%Y A212402 Row 1 is A032443
%K A212402 nonn,tabl
%O A212402 1,1
%A A212402 _R. H. Hardin_ May 14 2012