cp's OEIS Frontend

A213120 Number of binary arrays of length 2*n+2 with fewer than n ones in any length 2n subsequence (=less than 50% duty cycle).

%I A213120 #13 Oct 29 2012 07:29:29
%S A213120 1,10,54,252,1110,4748,19964,83024,342678,1406748,5751636,23443240,
%T A213120 95319484,386805112,1567130168,6340730552,25626393878,103472018492,
%U A213120 417449893988,1682982404072,6780908053268,27306234108392,109907864408648
%N A213120 Number of binary arrays of length 2*n+2 with fewer than n ones in any length 2n subsequence (=less than 50% duty cycle).
%C A213120 Row 3 of A213118.
%H A213120 R. H. Hardin, <a href="/A213120/b213120.txt">Table of n, a(n) for n = 1..210</a>
%F A213120 Recurrence: n*(5*n-13)*a(n) = 2*(20*n^2-67*n+40)*a(n-1) - 8*(2*n-5)*(5*n-8) * a(n-2). - _Vaclav Kotesovec_, Oct 19 2012
%F A213120 a(n) = 2^(2*n+1) - (15*n-8)*C(2*n-2,n-1)/n. - _Vaclav Kotesovec_, Oct 29 2012
%e A213120 Some solutions for n=3
%e A213120 ..0....0....0....0....1....1....0....0....0....0....0....0....0....1....0....1
%e A213120 ..0....1....0....0....0....0....0....1....0....0....0....0....1....1....0....0
%e A213120 ..0....1....1....0....1....1....0....0....0....0....0....1....0....0....1....0
%e A213120 ..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
%e A213120 ..0....0....0....0....0....0....1....1....0....0....0....1....0....0....0....1
%e A213120 ..1....0....1....0....0....0....0....0....0....1....0....0....0....0....0....0
%e A213120 ..0....0....0....0....0....0....0....0....1....1....0....0....1....0....0....1
%e A213120 ..0....1....0....0....0....1....1....0....0....0....1....0....1....1....1....0
%t A213120 Table[2^(2*n+1)-(15*n-8)*Binomial[2*n-2,n-1]/n,{n,1,20}] (* _Vaclav Kotesovec_, Oct 29 2012 *)
%K A213120 nonn
%O A213120 1,2
%A A213120 _R. H. Hardin_ Jun 05 2012