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 A270445 #15 Mar 18 2016 07:22:58 %S A270445 2,32,352,3712,38912,407552,4268032,44695552,468058112,4901568512, %T A270445 51329892352,537533612032,5629125066752,58948963008512, %U A270445 617321555034112,6464675252273152,67698958146732032,708952693724413952,7424248994345254912 %N A270445 Expansion of 2*x*(1+4*x) / (1-12*x+16*x^2). %C A270445 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 A270445 Colin Barker, <a href="/A270445/b270445.txt">Table of n, a(n) for n = 1..950</a> %H A270445 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (12,-16). %F A270445 a(n) = 12*a(n-1) - 16*a(n-2) for n>2. G.f.: 2*x*(1+4*x) / (1-12*x+16*x^2). - _Colin Barker_, Mar 17 2016 %F A270445 a(n) = (1+sqrt(5))^(2*n-1) + (1-sqrt(5))^(2*n-1). %e A270445 a(2) = 32 because (1 + sqrt(5))^3 + (1 - sqrt(5))^3 = 32. %o A270445 (PARI) Vec(2*x*(1+4*x)/(1-12*x+16*x^2) + O(x^50)) \\ _Colin Barker_, Mar 17 2016 %Y A270445 Cf. A077444, A087131. %K A270445 nonn,easy %O A270445 1,1 %A A270445 _Altug Alkan_, Mar 17 2016