A280072 - OEIS

%I #9 Aug 19 2020 16:35:42

%S 1,11,210,4180,83381,1663431,33185230,662041160,13207637961,

%T 263490718051,5256606723050,104868643742940,2092116268135741,

%U 41737456718971871,832657018111301670,16611402905507061520,331395401092029928721,6611296618935091512891

%N Indices of centered 11-gonal numbers (A060544) that are also 11-gonal numbers (A051682).

%C 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 Colin Barker, <a href="/A280072/b280072.txt">Table of n, a(n) for n = 1..750</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (21,-21,1).

%F a(n) = (6 - (3+sqrt(11))*(10+3*sqrt(11))^(-n) + (-3+sqrt(11))*(10+3*sqrt(11))^n)/12.

%F a(n) = 21*a(n-1) - 21*a(n-2) + a(n-3) for n>3.

%F G.f.: x*(1 - 10*x) / ((1 - x)*(1 - 20*x + x^2)).

%e 11 is in the sequence because the 11th centered 11-gonal number is 606, which is also the 12th 11-gonal number.

%t LinearRecurrence[{21,-21,1},{1,11,210},20] (* _Harvey P. Dale_, Aug 19 2020 *)

%o (PARI) Vec(x*(1 - 10*x) / ((1 - x)*(1 - 20*x + x^2)) + O(x^30)) \\ _Colin Barker_, Dec 25 2016

%Y Cf. A051682, A060544, A131215, A280071.

%K nonn,easy

%O 1,2

%A _Colin Barker_, Dec 25 2016