%I
%S 1,135,26125,5068051,983175705,190731018655,37000834443301,
%T 7177971150981675,1392489402456001585,270135766105313325751,
%U 52404946135028329194045,10166289414429390550318915,1972207741453166738432675401,382598135552499917865388708815
%N Indices of octagonal numbers which are also decagonal.
%C As n increases, this sequence is approximately geometric with common ratio r = lim(n>Infinity, a(n)/a(n1)) = (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*(160*x5*x^2) / ((1x)*(1194*x+x^2)).
%F a(n) = 194*a(n1)a(n2)64.
%F a(n) = 195*a(n1)195*a(n2)+a(n3).
%F a(n) = 1/24*((1+2*sqrt(3))*(2+sqrt(3))^(4*n3)+(12*sqrt(3))*(2sqrt(3))^(4*n3)+8).
%F a(n) = ceiling(1/24*(1+2*sqrt(3))*(2+sqrt(3))^(4*n3)).
%e The second octagonal number that is also decagonal is A000567(135) = 54405. Hence a(2) = 135.
%t LinearRecurrence[{195, 195, 1}, {1, 135, 26125}, 14]
%Y Cf. A203624, A203626, A001107, A000567.
%K nonn,easy
%O 1,2
%A _Ant King_, Jan 05 2012
