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%I #10 Dec 11 2016 13:13:36
%S 1,4,19,79,338,1427,6053,25628,108583,459931,1948354,8253271,34961561,
%T 148099316,627359147,2657535383,11257501522,47687540107,202007664157,
%U 855718193164,3624880442591,15355239954179,65045840274434
%N F(n+1)F(2n+2)+F(n)F(2n).
%C Let M be the matrix M(n,k)=F(k+1)*sum{j=0..n, (-1)^(n-j)C(n,j)C(j+1,k+1)}. a(n) gives the row sums of M^3.
%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (3,6,-3,-1).
%F G.f.: (1+x)*(1+x^2) / ( (x^2+4*x-1)*(x^2-x-1) ).
%F a(n)=(sqrt(5)+2)^n(sqrt(5)/5+3/5)-2^(-n-1)(sqrt(5)-1)^n(sqrt(5)/5+1/5)+ 2^(-n-1)(sqrt(5)+1)^n(sqrt(5)/5-1/5)(-1)^n+(sqrt(5)-2)^n(3/5-sqrt(5)/5)(-1)^n;
%F a(n) = (2*A163063(n) -A061084(n))/5. - _R. J. Mathar_, Jun 08 2016
%t Table[Fibonacci[n+1]Fibonacci[2n+2]+Fibonacci[n]Fibonacci[2n],{n,0,30}] (* or *) LinearRecurrence[{3,6,-3,-1},{1,4,19,79},30] (* _Harvey P. Dale_, Dec 11 2016 *)
%Y Cf. A000045, A037451.
%K easy,nonn
%O 0,2
%A _Paul Barry_, Sep 18 2006
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