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%I #16 Sep 25 2019 07:44:03
%S 5,125,4905,104845,2236945,43997205,839065625,15568306205,
%T 283472166945,5085221879845,90160039460905,1583296366510125,
%U 27584549361811505,477381553387733045,8214565750925426745,140656423431038828605,2398076730140587458625,40730410912379868020805,689465506509001244803145,11635911013748474608877645
%N a(n) = (4*n+1)*(2^(4*n+1)+(-1)^n*2^(2*n+1)+1).
%C A subsequence of one of the columns of the array described in A202624.
%H David J. Seal, <a href="https://doi.org/10.1017/S0308210500032479">The orders of the Fibonacci groups</a>, Proc. Roy. Soc. Edinburgh, Sect. A 92 (1982), no. 3-4, 181-192.
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (26,-65,-1480,-1040,6656,-4096).
%F a(0)=5, a(1)=125, a(2)=4905, a(3)=104845, a(4)=2236945, a(5)=43997205, a(n)=26*a(n-1)-65*a(n-2)-1480*a(n-3)-1040*a(n-4)+ 6656*a(n-5)- 4096*a(n-6). - _Harvey P. Dale_, May 23 2014
%F G.f.: 5*(1-x+396*x^2-1432*x^3+4000*x^4+1536*x^5)/(x-1)^2/(4*x+1)^2/(16*x-1)^2 . - _R. J. Mathar_, Sep 02 2017
%t Table[(4n+1)(2^(4n+1)+(-1)^n 2^(2n+1)+1),{n,0,20}] (* or *) LinearRecurrence[ {26,-65,-1480,-1040,6656,-4096},{5,125,4905,104845,2236945,43997205},20] (* _Harvey P. Dale_, May 23 2014 *)
%Y Cf. A202624.
%K nonn,easy
%O 0,1
%A _N. J. A. Sloane_, Dec 31 2011
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