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%I #18 May 31 2019 18:11:55
%S 0,0,128,1024,6656,53248,387072,3096576,24092672,192741376,1530822656,
%T 12246581248,97793998848,782351990784,6255953838080,50047630704640,
%U 400335237545984,3202681900367872,25620722214764544,204965777718116352,1639714493699194880,13117715949593559040,104941539947077173248,839532319576617385984
%N Total number of triangles in Cayley graph Cay(Z_{2^n}, QR*(2^n)).
%H Vincenzo Librandi, <a href="/A206278/b206278.txt">Table of n, a(n) for n = 3..1000</a>
%H Reinaldo E. Giudici and Aurora A. Olivieri, <a href="http://dx.doi.org/10.1016/S0012-365X(99)00229-0">Quadratic modulo 2n Cayley graphs</a>, Discrete Math. 215 (2000), no. 1-3, 73-79. See T(n) in Theorem 3.1.
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (8,20,-160,-64,512).
%F G.f.: 128*x^5*(32*x^2-1) / ((2*x-1)*(2*x+1)*(4*x-1)*(4*x+1)*(8*x-1)). - _Colin Barker_, Jul 23 2013
%p f:=n-> if n mod 2 = 1 then
%p (1/45)*(2^(3*(n-1))+5*2^(2*n-1)-7*2^(n+2));
%p else
%p (1/45)*(2^(3*(n-1))+5*2^(2*n)-7*2^(n+4));
%p fi;
%p [seq(f(n),n=3..40)];
%t CoefficientList[Series[128 x^2 (32 x^2 - 1) / ((2 x - 1) (2 x + 1) (4 x - 1) (4 x + 1) (8 x - 1)), {x, 0, 33}], x] (* _Vincenzo Librandi_, Aug 21 2016 *)
%t LinearRecurrence[{8,20,-160,-64,512},{0,0,128,1024,6656},30] (* _Harvey P. Dale_, May 31 2019 *)
%K nonn,easy
%O 3,3
%A _N. J. A. Sloane_, Feb 05 2012
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