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 A164541 #14 Feb 04 2023 12:59:13
%S A164541 1,15,89,519,3025,17631,102761,598935,3490849,20346159,118586105,
%T A164541 691170471,4028436721,23479449855,136848262409,797610124599,
%U A164541 4648812485185,27095264786511,157922776233881,920441392616775
%N A164541 a(n) = 6*a(n-1) - a(n-2) for n > 1; a(0) = 1, a(1) = 15.
%C A164541 Binomial transform of A164540. Third binomial transform of A164675. Inverse binomial transform of A164542.
%H A164541 Vincenzo Librandi, <a href="/A164541/b164541.txt">Table of n, a(n) for n = 0..155</a>
%H A164541 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (6, -1).
%F A164541 a(n) = 6*a(n-1) - a(n-2) for n > 1; a(0) = 1, a(1) = 15.
%F A164541 G.f: (1+9*x)/(1-6*x+x^2).
%F A164541 a(n) = ((1+3*sqrt(2))*(3+2*sqrt(2))^n + (1-3*sqrt(2))*(3-2*sqrt(2))^n)/2.
%t A164541 LinearRecurrence[{6,-1},{1,15},20] (* _Harvey P. Dale_, Feb 04 2023 *)
%o A164541 (Magma) Z<x>:=PolynomialRing(Integers()); N<r>:=NumberField(x^2-2); S:=[ ((1+3*r)*(3+2*r)^n+(1-3*r)*(3-2*r)^n)/2: n in [0..19] ]; [ Integers()!S[j]: j in [1..#S] ]; // _Klaus Brockhaus_, Aug 20 2009
%Y A164541 Cf. A164540, A164675, A164542.
%K A164541 nonn,easy
%O A164541 0,2
%A A164541 Al Hakanson (hawkuu(AT)gmail.com), Aug 15 2009
%E A164541 Edited and extended beyond a(5) by _Klaus Brockhaus_, Aug 20 2009