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 A098309 #13 Oct 28 2019 15:40:01 %S A098309 0,1,10,121,1440,17161,204490,2436721,29036160,345997201,4122930250, %T A098309 49129165801,585427059360,6975995546521,83126519498890, %U A098309 990542238440161,11803380341783040,140650021862956321,1675996882013692810,19971312562301357401,237979753865602596000 %N A098309 Unsigned member r = -10 of the family of Chebyshev sequences S_r(n) defined in A092184. %C A098309 ((-1)^(n+1))*a(n) = S_{-10}(n), n>=0, defined in A092184. %H A098309 Colin Barker, <a href="/A098309/b098309.txt">Table of n, a(n) for n = 0..900</a> %H A098309 <a href="/index/Ch#Cheby">Index entries for sequences related to Chebyshev polynomials.</a> %H A098309 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (11,11,-1). %F A098309 a(n) = (T(n, 6)-(-1)^n)/7, with Chebyshev's polynomials of the first kind evaluated at x=6: T(n, 6)=A023038(n)=((6+sqrt(35))^n + (6-sqrt(35))^n)/2. %F A098309 a(n) = 12*a(n-1)-a(n-2)+2*(-1)^(n+1), n>=2, a(0)=0, a(1)=1. %F A098309 a(n) = 11*a(n-1) + 11*a(n-2) - a(n-3), n>=3, a(0)=0, a(1)=1, a(2)=10. %F A098309 G.f.: x*(1-x)/((1+x)*(1-12*x+x^2)) = x*(1-x)/(1-11*x-11*x^2+x^3) (from the Stephan link, see A092184). %F A098309 a(n) = (-2*(-1)^n + (6-sqrt(35))^n + (6+sqrt(35))^n) / 14. - _Colin Barker_, Jan 31 2017 %t A098309 LinearRecurrence[{11,11,-1},{0,1,10},30] (* _Harvey P. Dale_, Oct 28 2019 *) %o A098309 (PARI) concat(0, Vec(x*(1-x)/(1-11*x-11*x^2+x^3) + O(x^30))) \\ _Colin Barker_, Jan 31 2017 %K A098309 nonn,easy %O A098309 0,3 %A A098309 _Wolfdieter Lang_, Oct 18 2004