%I #7 Aug 01 2015 10:02:27
%S 1,117,22625,4389061,851455137,165177907445,32043662589121,
%T 6216305364381957,1205931197027510465,233944435917972648181,
%U 45384014636889666236577,8804264895120677277247685,1707982005638774502119814241,331339704829027132733966714997
%N Indices of decagonal numbers which are also octagonal.
%C As n increases, this sequence is approximately geometric with common ratio r = lim(n->Infinity, a(n)/a(n-1)) = (2+sqrt(3))^4 = 97+56*sqrt(3).
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (195, -195, 1).
%F G.f.: x*(1-78*x+5*x^2) / ((1-x)*(1-194*x+x^2)).
%F a(n) = 194*a(n-1)-a(n-2)-72.
%F a(n) = 195*a(n-1)-195*a(n-2)+a(n-3).
%F a(n) = 1/48*((sqrt(3)+6)*(2+sqrt(3))^(4*n-3)-(sqrt(3)-6)*(2-sqrt(3))^(4*n-3)+18).
%F a(n) = ceiling(1/48*(sqrt(3)+6)*(2+sqrt(3))^(4*n-3)).
%e The second decagonal number that is also octagonal is A001107(117) = 54405. Hence a(2) = 117.
%t LinearRecurrence[{195, -195, 1}, {1, 117, 22625}, 14]
%Y Cf. A203624, A203625, A001107, A000567.
%K nonn,easy
%O 1,2
%A _Ant King_, Jan 05 2012