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%I #12 Dec 25 2016 11:51:37
%S 1,11,191,3421,61381,1101431,19764371,354657241,6364065961,
%T 114198530051,2049209474951,36771572019061,659839086868141,
%U 11840331991607471,212466136762066331,3812550129725586481,68413436198298490321,1227629301439647239291,22028913989715351816911
%N Indices of 10-gonal numbers (A001107) that are also centered 10-gonal numbers (A062786).
%C Also positive integers x in the solutions to 4*x^2 - 5*y^2 - 3*x + 5*y - 1 = 0, the corresponding values of y being A133273.
%H Colin Barker, <a href="/A280070/b280070.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 (19,-19,1).
%F a(n) = (6 + (5+2*sqrt(5))*(9+4*sqrt(5))^(-n) + (5-2*sqrt(5))*(9+4*sqrt(5))^n)/16.
%F a(n) = 19*a(n-1) - 19*a(n-2) + a(n-3) for n>3.
%F G.f.: x*(1 - 8*x + x^2) / ((1 - x)*(1 - 18*x + x^2)).
%e 11 is in the sequence because the 11th 10-gonal number is 451, which is also the 10th centered 10-gonal number.
%o (PARI) Vec(x*(1 - 8*x + x^2) / ((1 - x)*(1 - 18*x + x^2)) + O(x^30))
%Y Cf. A001107, A062786, A128922, A133273.
%K nonn,easy
%O 1,2
%A _Colin Barker_, Dec 25 2016
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