This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A212405 #12 Jun 02 2025 07:57:19
%S A212405 13,57,236,959,3872,15586,62632,251419,1008536,4043582,16206152,
%T A212405 64933782,260114976,1041797124,4171943056,16704821779,66880877896,
%U A212405 267747443494,1071808583176,4290243456514,17172082337536,68729504287324
%N A212405 Number of binary arrays of length 2*n+3 with no more than n ones in any length 2n subsequence (=50% duty cycle).
%C A212405 Row 4 of A212402
%H A212405 R. H. Hardin, <a href="/A212405/b212405.txt">Table of n, a(n) for n = 1..210</a>
%F A212405 Recurrence (for n>3): n^2*a(n) = 2*(4*n^2-3*n-5)*a(n-1) - 8*(n+1)*(2*n-5)*a(n-2). - _Vaclav Kotesovec_, Oct 19 2012
%F A212405 a(n) = 2^(2*n+2) - (3*n+1)/n * C(2*n-2,n-1), for n>1. - _Vaclav Kotesovec_, Oct 28 2012
%e A212405 Some solutions for n=3
%e A212405 ..1....0....0....1....0....0....1....1....1....0....1....0....1....0....0....0
%e A212405 ..0....0....0....1....0....0....0....0....0....0....1....0....0....0....1....1
%e A212405 ..1....1....0....1....1....0....1....0....1....1....1....0....0....1....0....0
%e A212405 ..1....0....0....0....0....0....0....1....0....0....0....0....0....0....1....1
%e A212405 ..0....1....0....0....1....0....0....0....0....1....0....0....1....0....1....0
%e A212405 ..0....0....1....0....0....1....1....0....1....1....0....0....0....0....0....1
%e A212405 ..0....0....1....0....1....0....1....0....0....0....1....0....0....0....0....0
%e A212405 ..1....0....1....1....0....1....0....1....0....0....0....1....1....0....1....0
%e A212405 ..1....1....0....1....0....1....1....1....1....1....1....0....0....0....0....0
%t A212405 Flatten[{13,Table[2^(2*n+2)-(3*n+1)/n*Binomial[2*n-2,n-1],{n,2,20}]}] (* _Vaclav Kotesovec_, Oct 28 2012 *)
%K A212405 nonn
%O A212405 1,1
%A A212405 _R. H. Hardin_ May 14 2012