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 A161729 #23 Aug 31 2023 09:52:34
%S A161729 1,16,204,2432,28304,326400,3750592,43036672,493555968,5658988544,
%T A161729 64878906368,743795097600,8527018430464,97754949812224,
%U A161729 1120674238611456,12847530427547648,147285426432966656,1688495240694988800,19357081676605554688,221911554309549457408,2544016621769302474752
%N A161729 a(n) = ((4+sqrt(3))*(8+2*sqrt(3))^n-(4-sqrt(3))*(8-2*sqrt(3))^n)/(2*sqrt(3)).
%C A161729 Eighth binomial transform of A162466.
%H A161729 Harvey P. Dale, <a href="/A161729/b161729.txt">Table of n, a(n) for n = 0..943</a>
%H A161729 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (16,-52).
%F A161729 a(n) = 16*a(n-1) - 52(n-2) for n > 1; a(0) = 1, a(1) = 16.
%F A161729 G.f.: 1/(1 - 16*x + 52*x^2). - _Klaus Brockhaus_, Jun 19 2009
%F A161729 a(n) = 2^n*A153594(n). - _M. F. Hasler_, Dec 03 2014
%F A161729 E.g.f.: exp(8*x)*(3*cosh(2*sqrt(3)*x) + 4*sqrt(3)*sinh(2*sqrt(3)*x))/3. - _Stefano Spezia_, Dec 31 2022
%t A161729 Join[{a=1,b=16},Table[c=16*b-52*a;a=b;b=c,{n,40}]] (* _Vladimir Joseph Stephan Orlovsky_, Feb 08 2011 *)
%t A161729 LinearRecurrence[{16,-52},{1,16},20] (* _Harvey P. Dale_, Dec 23 2020 *)
%o A161729 (PARI) F=nfinit(x^2-3); for(n=0, 17, print1(nfeltdiv(F, ((4+x)*(8+2*x)^n-(4-x)*(8-2*x)^n), (2*x))[1], ",")) \\ _Klaus Brockhaus_, Jun 19 2009
%o A161729 (PARI) Vec(1/(1-16*x+52*x^2)+O(x^25)) \\ _M. F. Hasler_, Dec 03 2014
%Y A161729 Cf. A162466, A161728, A153594.
%K A161729 nonn,easy
%O A161729 0,2
%A A161729 Al Hakanson (hawkuu(AT)gmail.com), Jun 17 2009
%E A161729 Extended beyond a(5) by _Klaus Brockhaus_, Jun 19 2009
%E A161729 Edited by _Klaus Brockhaus_, Jul 05 2009, and _M. F. Hasler_, Dec 03 2014