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 A083334 #29 Dec 14 2024 13:48:18
%S A083334 1,6,17,47,179,414,1723,3793,16201,35166,151337,327167,1411019,
%T A083334 3046854,13148803,28383073,122510161,264425526,1141401857,2463529487,
%U A083334 10634068259,22951715694,99073772683,213832351153,923033565721
%N A083334 a(n) = 12*a(n-2) - 25*a(n-4) with initial terms 1,6,17,47.
%C A083334 a(n)/A083335(n) converges to sqrt(11).
%H A083334 Harvey P. Dale, <a href="/A083334/b083334.txt">Table of n, a(n) for n = 0..1000</a>
%H A083334 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,12,0,-25).
%F A083334 G.f.: (1 + 6*x + 5*x^2 - 25*x^3) / (1 - 12*x^2 + 25*x^4).
%F A083334 a(n) = (x^(n+1) + (-1)^(n+1)*(x-2)^(n+1))/2^ceiling(n/2 + 1) where x = 1 + sqrt(11). - _Ben Paul Thurston_, Aug 30 2006 [edited by _Jon E. Schoenfield_, Jun 25 2019]
%t A083334 CoefficientList[Series[(1+6x+5x^2-25x^3)/(1-12x^2+25x^4), {x, 0, 10}], x]
%t A083334 LinearRecurrence[{0,12,0,-25},{1,6,17,47},30] (* _Harvey P. Dale_, Oct 15 2012 *)
%Y A083334 Cf. A010468 (sqrt(11)), A083335.
%K A083334 easy,nonn
%O A083334 0,2
%A A083334 Mario Catalani (mario.catalani(AT)unito.it), Apr 26 2003