A213124 - OEIS

%I #16 May 11 2019 02:21:45

%S 1,36,324,1996,10154,47448,211888,920744,3930286,16570608,69240296,

%T 287379592,1186575444,4879222736,19997163520,81735122832,333327346838,

%U 1356783786272,5513802056888,22376476701512,90701190829388

%N Number of binary arrays of length 2*n+6 with fewer than n ones in any length 2n subsequence (=less than 50% duty cycle).

%H R. H. Hardin, <a href="/A213124/b213124.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical (for n>=5): n*(143*n^3 - 1584*n^2 + 5761*n - 6880)*a(n) = 2*(572*n^4 - 6765*n^3 + 27961*n^2 - 46078*n + 23040)*a(n-1) - 8*(2*n-9)*(143*n^3 - 1155*n^2 + 3022*n - 2560)*a(n-2). - _Vaclav Kotesovec_, Nov 20 2012

%F Empirical (for n>=4): a(n) = 2^(2*n+5) - 12*(1001*n^3 - 4697*n^2 + 6510*n - 2560) * C(2*n-7, n-4) / ((n-2)*(n-1)*n). - _Vaclav Kotesovec_, Nov 20 2012

%e Some solutions for n=3:

%e   1  0  0  1  0  1  1  0  0  0  0  0  0  0  1  0

%e   0  1  1  1  0  0  0  0  0  0  1  1  0  1  0  0

%e   0  1  1  0  0  0  0  0  0  0  0  1  1  1  0  0

%e   0  0  0  0  1  0  0  1  1  1  1  0  1  0  0  0

%e   0  0  0  0  1  0  0  0  0  0  0  0  0  0  0  0

%e   1  0  0  0  0  0  1  0  0  0  0  0  0  0  0  0

%e   0  0  0  0  0  1  0  0  0  0  0  0  0  0  1  1

%e   1  0  0  0  0  0  0  1  0  0  0  0  0  1  0  1

%e   0  0  1  0  0  0  0  0  0  0  0  1  1  1  1  0

%e   0  1  0  1  1  0  0  0  1  0  1  1  0  0  0  0

%e   0  0  1  1  0  0  0  0  0  1  0  0  0  0  0  0

%e   1  0  0  0  0  1  0  1  1  1  1  0  0  0  0  0

%p #verified first terms (holds for all n<=210). - _Vaclav Kotesovec_, Nov 20 2012

%p with(gfun): A213124:= rectoproc({a(3)=324, a(4)=1996, n*(143*n^3-1584*n^2+5761*n-6880)*a(n) = 2*(572*n^4-6765*n^3+27961*n^2-46078*n+23040)*a(n-1) - 8*(2*n-9)*(143*n^3-1155*n^2+3022*n-2560)*a(n-2)},a(n),remember): 1,36,seq(A213124(n),n=3..20); A213124(210);

%Y Row 7 of A213118.

%K nonn

%O 1,2

%A _R. H. Hardin_, Jun 05 2012