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A167780 Subsequence of A167708 whose indices are 0 mod 5, that is, a(n) = A167708(5n+5).

%I A167780 #22 Jun 27 2016 18:21:42
%S A167780 959,326050,110856041,37690727890,12814736626559,4356972762302170,
%T A167780 1481357924446111241,503657337338915519770,171242013337306830610559,
%U A167780 58221780877346983492070290,19795234256284637080473288041
%N A167780 Subsequence of A167708 whose indices are 0 mod 5, that is, a(n) = A167708(5n+5).
%H A167780 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (340, -1).
%F A167780 a(n+2) = 340*a(n+1) - a(n).
%F A167780 a(n+1) = 170*a(n) + 39*sqrt(19*a(n)^2 - 1539).
%F A167780 G.f.: (959 - 10*z)/(1 - 340*z + z^2).
%F A167780 a(n) = (220*sqrt(19) + 959)/2*(170 + 39*sqrt(19))^n + (-220*sqrt(19) + 959)/2*(170 - 39*sqrt(19))^n. - _Richard Choulet_, Nov 13 2009
%F A167780 a(n) = 10*cosh(x*log(170 + 39*Sqrt[19])) - Sqrt[19]*sinh(x*log(170 + 39*Sqrt[19])). - _Harvey P. Dale_, Aug 06 2013
%e A167780 a(0) = A167708(5) = 959, a(1) = A167708(10) = 326050,...
%p A167780 u(0):=959:u(1):=326050:for n from 0 to 20 do u(n+2):=340*u(n+1)-u(n):od:seq(u(n),n=0..20); taylor(((959+326050*z-959*z*340)/(1-340*z+z^2)),z=0,20); for n from 0 to 20 do u(n):=simplify((220*sqrt(19)+959)/2*(170+39*sqrt(19))^(n)+(-220*sqrt(19)+959)/2*(170-39*sqrt(19))^(n)):od:seq(u(n),n=0..20);
%t A167780 LinearRecurrence[{340,-1}, {959,326050}, 20] (* _Harvey P. Dale_, Aug 06 2013 *)
%Y A167780 Cf. A167708, A167709, A167774, A167775, A167778, A167779.
%K A167780 easy,nonn
%O A167780 0,1
%A A167780 _Richard Choulet_, Nov 11 2009