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 A080880 #12 Jul 31 2015 12:24:51
%S A080880 1,2,2,5,6,17,22,65,86,257,342,1025,1366,4097,5462,16385,21846,65537,
%T A080880 87382,262145,349526,1048577,1398102,4194305,5592406,16777217,
%U A080880 22369622,67108865,89478486,268435457,357913942,1073741825,1431655766,4294967297
%N A080880 a(n)*a(n+3) - a(n+1)*a(n+2) = 2^n, given a(0)=1, a(1)=2, a(2)=2.
%H A080880 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0, 5, 0, -4).
%F A080880 a(2n)=(4^n+2)/3, a(2n+1)=4^n+1.
%F A080880 G.f.: (-5*x^3 - 3*x^2 + 2*x + 1)/(4*x^4 - 5*x^2 + 1)
%F A080880 a(n) = 5/6 + 5/12*2^n - 1/6*( - 1)^n - 1/12*( - 2)^n [From _Richard Choulet_, Dec 07 2008]
%F A080880 a(n + 4) = 5*a(n + 2) - 4*a(n) [From _Richard Choulet_, Dec 06 2008]
%t A080880 LinearRecurrence[{0,5,0,-4},{1,2,2,5},40] (* _Harvey P. Dale_, Nov 30 2012 *)
%Y A080880 Cf. A080876, A080877, A080878, A080879, A080881, A080882.
%K A080880 nonn
%O A080880 0,2
%A A080880 _Paul D. Hanna_, Feb 22 2003
%E A080880 More terms from _Ralf Stephan_, Jul 25 2003