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 A164543 #12 Sep 08 2022 08:45:47 %S A164543 1,17,153,1241,9809,76993,603177,4722889,36974881,289459697, %T A164543 2266023993,17739425081,138871842929,1087148202913,8510660699337, %U A164543 66625087543849,521569643549761,4083069947252177,31964015532175833,250227966218471321 %N A164543 a(n) = 10*a(n-1) - 17*a(n-2) for n > 1; a(0) = 1, a(1) = 17. %C A164543 Binomial transform of A164542. Fifth binomial transform of A164675. %H A164543 Vincenzo Librandi, <a href="/A164543/b164543.txt">Table of n, a(n) for n = 0..144</a> %H A164543 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (10, -17). %F A164543 a(n) = 10*a(n-1) - 17*a(n-2) for n > 1; a(0) = 1, a(1) = 17. %F A164543 G.f.: (1+7*x)/(1-10*x+17*x^2). %F A164543 a(n) = ((1+3*sqrt(2))*(5+2*sqrt(2))^n + (1-3*sqrt(2))*(5-2*sqrt(2))^n)/2. %o A164543 (Magma) Z<x>:=PolynomialRing(Integers()); N<r>:=NumberField(x^2-2); S:=[ ((1+3*r)*(5+2*r)^n+(1-3*r)*(5-2*r)^n)/2: n in [0..18] ]; [ Integers()!S[j]: j in [1..#S] ]; // _Klaus Brockhaus_, Aug 20 2009 %Y A164543 Cf. A164542, A164675. %K A164543 nonn,easy %O A164543 0,2 %A A164543 Al Hakanson (hawkuu(AT)gmail.com), Aug 15 2009 %E A164543 Edited and extended beyond a(5) by _Klaus Brockhaus_, Aug 20 2009