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 A280072 #9 Aug 19 2020 16:35:42 %S A280072 1,11,210,4180,83381,1663431,33185230,662041160,13207637961, %T A280072 263490718051,5256606723050,104868643742940,2092116268135741, %U A280072 41737456718971871,832657018111301670,16611402905507061520,331395401092029928721,6611296618935091512891 %N A280072 Indices of centered 11-gonal numbers (A060544) that are also 11-gonal numbers (A051682). %C A280072 Also positive integers y in the solutions to 9*x^2 - 11*y^2 - 7*x + 11*y - 2 = 0, the corresponding values of x being A280071. %H A280072 Colin Barker, <a href="/A280072/b280072.txt">Table of n, a(n) for n = 1..750</a> %H A280072 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (21,-21,1). %F A280072 a(n) = (6 - (3+sqrt(11))*(10+3*sqrt(11))^(-n) + (-3+sqrt(11))*(10+3*sqrt(11))^n)/12. %F A280072 a(n) = 21*a(n-1) - 21*a(n-2) + a(n-3) for n>3. %F A280072 G.f.: x*(1 - 10*x) / ((1 - x)*(1 - 20*x + x^2)). %e A280072 11 is in the sequence because the 11th centered 11-gonal number is 606, which is also the 12th 11-gonal number. %t A280072 LinearRecurrence[{21,-21,1},{1,11,210},20] (* _Harvey P. Dale_, Aug 19 2020 *) %o A280072 (PARI) Vec(x*(1 - 10*x) / ((1 - x)*(1 - 20*x + x^2)) + O(x^30)) \\ _Colin Barker_, Dec 25 2016 %Y A280072 Cf. A051682, A060544, A131215, A280071. %K A280072 nonn,easy %O A280072 1,2 %A A280072 _Colin Barker_, Dec 25 2016