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%I #18 Mar 07 2020 00:49:23
%S 0,14,24,14,0,38,168,350,528,854,1848,4238,8736,16646,31944,64190,
%T 131376,265142,526680,1044974,2088768,4193126,8404200,16795166,
%U 33541200,67059734,134195064,268511054,536991840,1073711558,2147211528
%N Number of rational points of Klein curve over GF(2^n).
%D N. Elkies, The Klein quartic in number theory, pp. 51-101 of S. Levy, ed., The Eightfold Way, Cambridge Univ. Press, 1999. See p. 77 eq. (3.13), (3.14).
%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (4,-7,8,-4).
%F a(n) = 2^n + 1 - 3*(a^n + b^n), where a, b are roots of X^2 - X + 2 = 0.
%F From _Colin Barker_, Aug 01 2013: (Start)
%F a(n) = 4*a(n-1) - 7*a(n-2) + 8*a(n-3) - 4*a(n-4).
%F G.f.: 2*x^2*(8*x^2-16*x+7) / ((x-1)*(2*x-1)*(2*x^2-x+1)). (End)
%e G.f. = 14*x^2 + 24*x^3 + 14*x^4 + 38*x^6 + 168*x^7 + 350*x^8 + 528*x^9 + ...
%t LinearRecurrence[{4,-7,8,-4},{0,14,24,14},40] (* _Harvey P. Dale_, May 09 2017 *)
%o (PARI) {a(n) = if( n<1, 0, 2^n + 1 - 3 * polsym(x^2 - x + 2, n)[n+1])}; /* _Michael Somos_, Nov 09 2014 */
%Y Cf. A002249.
%K nonn
%O 1,2
%A _N. J. A. Sloane_
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