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%I #25 Jun 09 2020 12:26:20
%S 2,20,152,1136,8480,63296,472448,3526400,26321408,196465664,
%T 1466439680,10945654784,81699479552,609813217280,4551707820032,
%U 33974409691136,253588446248960,1892809931227136,14128125664821248,105453765593661440
%N Expansion of 2*(1+2*x) / (1-8*x+4*x^2).
%C If p is an odd prime, a((p+1)/2) == 2 mod p. In other words, a((p+1)/2) - 2^p is divisible by p where p is an odd prime.
%H Harvey P. Dale, <a href="/A270444/b270444.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (8, -4).
%F G.f.: 2*(1+2*x)/(1-8*x+4*x^2).
%F a(n) = (1+sqrt(3))^(2*n-1) + (1-sqrt(3))^(2*n-1).
%F a(n) = 2 * A107903(n-1).
%e a(2) = 20 because (1 + sqrt(3))^3 + (1 - sqrt(3))^3 = 20.
%t CoefficientList[Series[2(1+2x)/(1-8x+4x^2),{x,0,30}],x] (* or *) LinearRecurrence[{8,-4},{2,20},30] (* _Harvey P. Dale_, Jun 09 2020 *)
%o (PARI) Vec(2*(1+2*x)/(1-8*x+4*x^2) + O(x^100))
%Y Cf. A077444, A080040, A080041, A107903.
%K nonn
%O 1,1
%A _Altug Alkan_, Mar 17 2016
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