cp's OEIS Frontend

A213118 T(n,k)=Number of binary arrays of length n+2*k-1 with fewer than k ones in any length 2k subsequence (=less than 50% duty cycle).

%I A213118 #6 Jun 02 2025 08:00:53
%S A213118 1,5,1,22,7,1,93,34,10,1,386,151,54,14,1,1586,646,252,86,19,1,6476,
%T A213118 2710,1110,424,136,26,1,26333,11236,4748,1926,714,212,36,1,106762,
%U A213118 46231,19964,8404,3354,1198,324,50,1,431910,189214,83024,35836,14946,5842,1996,498
%N A213118 T(n,k)=Number of binary arrays of length n+2*k-1 with fewer than k ones in any length 2k subsequence (=less than 50% duty cycle).
%C A213118 Table starts
%C A213118 .1..5..22...93...386..1586...6476...26333..106762...431910...1744436...7036530
%C A213118 .1..7..34..151...646..2710..11236...46231..189214...771442...3136156..12720982
%C A213118 .1.10..54..252..1110..4748..19964...83024..342678..1406748...5751636..23443240
%C A213118 .1.14..86..424..1926..8404..35836..150604..626726..2589844..10646676..43594464
%C A213118 .1.19.136..714..3354.14946..64664..274676.1152494..4793874..19813536..81495084
%C A213118 .1.26.212.1198..5842.26630.116992..502492.2126238..8903350..36998056.152862180
%C A213118 .1.36.324.1996.10154.47448.211888..920744.3930286.16570608..69240296.287379592
%C A213118 .1.50.498.3292.17578.84424.383728.1688200.7272622.30880672.129768616.541108840
%H A213118 R. H. Hardin, <a href="/A213118/b213118.txt">Table of n, a(n) for n = 1..4938</a>
%e A213118 Some solutions for n=3 k=4
%e A213118 ..0....0....1....0....1....1....1....0....0....1....1....0....0....0....1....0
%e A213118 ..1....0....1....0....1....0....0....0....0....0....0....0....0....1....0....0
%e A213118 ..1....0....0....1....1....1....0....0....1....1....1....0....0....0....0....0
%e A213118 ..1....0....0....0....0....0....0....1....1....1....0....1....0....0....1....1
%e A213118 ..0....0....0....0....0....1....1....0....0....0....1....0....0....0....0....0
%e A213118 ..0....1....0....0....0....0....1....0....1....0....0....0....1....1....0....1
%e A213118 ..0....1....0....1....0....0....0....1....0....0....0....1....0....1....0....0
%e A213118 ..0....0....0....1....0....0....0....0....0....0....0....0....0....0....1....0
%e A213118 ..0....0....0....0....1....0....1....0....0....0....0....1....1....0....1....1
%e A213118 ..1....1....1....0....0....0....0....0....0....0....1....0....1....1....0....0
%Y A213118 Column 2 is A003269(n+7)
%Y A213118 Column 3 is A133523(n+5)
%Y A213118 Row 1 is A000346(n-1)
%K A213118 nonn,tabl
%O A213118 1,2
%A A213118 _R. H. Hardin_ Jun 05 2012