This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A270444 #25 Jun 09 2020 12:26:20
%S A270444 2,20,152,1136,8480,63296,472448,3526400,26321408,196465664,
%T A270444 1466439680,10945654784,81699479552,609813217280,4551707820032,
%U A270444 33974409691136,253588446248960,1892809931227136,14128125664821248,105453765593661440
%N A270444 Expansion of 2*(1+2*x) / (1-8*x+4*x^2).
%C A270444 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 A270444 Harvey P. Dale, <a href="/A270444/b270444.txt">Table of n, a(n) for n = 1..1000</a>
%H A270444 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (8, -4).
%F A270444 G.f.: 2*(1+2*x)/(1-8*x+4*x^2).
%F A270444 a(n) = (1+sqrt(3))^(2*n-1) + (1-sqrt(3))^(2*n-1).
%F A270444 a(n) = 2 * A107903(n-1).
%e A270444 a(2) = 20 because (1 + sqrt(3))^3 + (1 - sqrt(3))^3 = 20.
%t A270444 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 A270444 (PARI) Vec(2*(1+2*x)/(1-8*x+4*x^2) + O(x^100))
%Y A270444 Cf. A077444, A080040, A080041, A107903.
%K A270444 nonn
%O A270444 1,1
%A A270444 _Altug Alkan_, Mar 17 2016