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A167774 Subsequence of A167708 whose indices are congruent to 1 mod 5, i.e., a(n) = A167708(5*n+1).

%I A167774 #23 Feb 11 2024 05:16:14
%S A167774 9,1530,520191,176863410,60133039209,20445056467650,6951259065961791,
%T A167774 2363407637370541290,803551645446918076809,273205196044314775573770,
%U A167774 92888963103421576777004991,31581974249967291789406123170,10737778356025775786821304872809
%N A167774 Subsequence of A167708 whose indices are congruent to 1 mod 5, i.e., a(n) = A167708(5*n+1).
%H A167774 G. C. Greubel, <a href="/A167774/b167774.txt">Table of n, a(n) for n = 0..250</a>
%H A167774 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (340,-1).
%F A167774 Recurrence formulas: a(n+2) = 340*a(n+1) - a(n) or a(n+1) = 170*a(n) + 39*sqrt(19*a(n)^2 - 1539).
%F A167774 G.f.: (9 - 1530*z)/(1 - 340*z + z^2).
%F A167774 a(n) = (9/2)*(170 + 39*sqrt(19))^(n) + (9/2)*(170 - 39*sqrt(19))^(n).
%F A167774 a(n) = 9*A114048(n+1). - _R. J. Mathar_, Feb 19 2016
%e A167774 a(0)=A167708(1)=9, a(1)=A167708(6)=1530.
%p A167774 u(0):=9:for n from 0 to 20 do u(n+1):=170*u(n)+39*sqrt(19*u(n)^2-1539):od:seq(u(n),n=0..20); taylor(((9+1530*z-9*z*340)/(1-340*z+z^2)),z=0,20);
%t A167774 LinearRecurrence[{340, -1}, {9, 1530}, 50] (* _G. C. Greubel_, Jun 23 2016 *)
%o A167774 (Magma) I:=[9, 1530]; [n le 2 select I[n] else 340*Self(n-1)-Self(n-2): n in [1..20]]; // _Vincenzo Librandi_, Jun 24 2016
%Y A167774 Cf. A114048, A167708, A167709, A167775, A167778, A167779, A167780.
%K A167774 easy,nonn
%O A167774 0,1
%A A167774 _Richard Choulet_, Nov 11 2009