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 A161728 #11 Dec 31 2022 13:39:59 %S A161728 1,7,43,253,1465,8431,48403,277621,1591729,9124759,52305595,299822893, %T A161728 1718610409,9851185663,56467549987,323674986277,1855321740385, %U A161728 10634799101479,60959210186827,349421293175389,2002900612974361,11480728092514831,65808116771451955,377215468968922837 %N A161728 a(n) = ((3+sqrt(3))*(4+sqrt(3))^n-(3-sqrt(3))*(4-sqrt(3))^n)/sqrt(12). %C A161728 Fourth binomial transform of A162436, inverse binomial transform of A162272. %C A161728 The inverse binomial transform yields A030192. The binomial transform yields A162272. - _R. J. Mathar_, Jul 07 2009 %H A161728 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (8,-13). %F A161728 a(n) = 8*a(n-1) - 13(n-2) for n > 1; a(0) = 1, a(1) = 7. %F A161728 G.f.: (1 - x)/(1 - 8*x + 13*x^2). - _Klaus Brockhaus_, Jun 19 2009 %F A161728 E.g.f.: exp(4*x)*(cosh(sqrt(3)*x) + sqrt(3)*sinh(sqrt(3)*x)). - _Stefano Spezia_, Dec 31 2022 %o A161728 (PARI) F=nfinit(x^2-3); for(n=0, 20, print1(nfeltdiv(F, ((3+x)*(4+x)^n-(3-x)*(4-x)^n), (2*x))[1], ",")) \\ _Klaus Brockhaus_, Jun 19 2009 %o A161728 (PARI) Vec((1-x)/(1-8*x+13*x^2)+O(x^25)) \\ _M. F. Hasler_, Dec 03 2014 %Y A161728 Cf. A162436, A162272, A030192, A161729. %K A161728 nonn,easy %O A161728 0,2 %A A161728 Al Hakanson (hawkuu(AT)gmail.com), Jun 17 2009 %E A161728 Extended beyond a(5) by _Klaus Brockhaus_, Jun 19 2009 %E A161728 Edited by _Klaus Brockhaus_, Jul 05 2009; _M. F. Hasler_, Dec 03 2014