cp's OEIS Frontend

A212404 Number of binary arrays of length 2*n+2 with no more than n ones in any length 2n subsequence (=50% duty cycle).

%I A212404 #12 Jun 02 2025 07:57:13
%S A212404 8,33,132,527,2104,8402,33560,134075,535728,2140910,8556568,34201078,
%T A212404 136713872,546528612,2184925808,8735357267,34925461088,139642914902,
%U A212404 558353310488,2232601256162,8927375430608,35698163696252,142750104755408
%N A212404 Number of binary arrays of length 2*n+2 with no more than n ones in any length 2n subsequence (=50% duty cycle).
%C A212404 Row 3 of A212402
%H A212404 R. H. Hardin, <a href="/A212404/b212404.txt">Table of n, a(n) for n = 1..210</a>
%F A212404 Recurrence (for n>4): (n-4)*n*a(n) = 2*(n-1)*(4*n-15)*a(n-1) - 8*(n-3)*(2*n-5)*a(n-2). - _Vaclav Kotesovec_, Oct 19 2012
%F A212404 a(n) = 2^(2*n+1) + C(2*n-2,n). - _Vaclav Kotesovec_, Oct 28 2012
%e A212404 Some solutions for n=3
%e A212404 ..0....0....0....1....0....1....0....0....0....1....0....0....1....1....1....0
%e A212404 ..0....0....1....0....0....0....1....1....0....0....1....1....0....0....0....0
%e A212404 ..1....1....0....1....1....0....1....0....0....0....1....0....0....0....1....1
%e A212404 ..1....0....1....0....1....0....0....0....0....1....0....0....0....1....0....0
%e A212404 ..1....0....1....1....0....1....0....1....1....1....0....1....0....0....0....1
%e A212404 ..0....1....0....0....0....1....1....0....0....0....0....0....0....1....0....0
%e A212404 ..0....1....0....0....1....1....0....0....0....0....0....1....1....0....0....0
%e A212404 ..0....0....1....0....0....0....1....1....1....1....1....0....0....1....1....1
%t A212404 Flatten[{8,33,RecurrenceTable[{(n-4)*n*a[n]==2*(n-1)*(4*n-15)*a[n-1]-8*(n-3)*(2*n-5)*a[n-2],a[3]==132,a[4]==527},a,{n,3,20}]}] (* _Vaclav Kotesovec_, Oct 19 2012 *)
%t A212404 Table[2^(2*n+1)+Binomial[2*n-2,n],{n,1,20}] (* _Vaclav Kotesovec_, Oct 28 2012 *)
%K A212404 nonn
%O A212404 1,1
%A A212404 _R. H. Hardin_ May 14 2012