%I #18 Sep 08 2022 08:45:48

%S 105,35634,12115455,4119219066,1400522366985,476173485555834,

%T 161897584566616575,55044702579164079666,18715036979331220469865,

%U 6363057528270035795674434,2163420844574832839308837695,735556724097914895329209141866,250087122772446489579091799396745

%N Subsequence of A167708 whose indices are congruent to 4 mod 5, i.e., a(n) = A167708(5n+4).

%H G. C. Greubel, <a href="/A167779/b167779.txt">Table of n, a(n) for n = 0..250</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (340,-1).

%F a(n+2) = 340*a(n+1) - a(n).

%F a(n+1) = 170*a(n) + 39*sqrt(19*a(n)^2 - 1539).

%F G.f.: (105 - 66*z)/(1 - 340*z + z^2).

%F a(n) = ((105 + 24*sqrt(19))/2)*(170 + 39*sqrt(19))^(n) + ((105 - 24*sqrt(19) )/2)*(170 - 39*sqrt(19))^(n).

%e a(0) = A167708(4) = 105, a(1) = A167708(9) = 35634, ...

%p u(0):=105:u(1):=35634:for n from 0 to 20 do u(n+2):=340*u(n+1)-u(n):od:seq(u(n),n=0..20); taylor(((105+35634*z-105*z*340)/(1-340*z+z^2)),z=0,20); for n from 0 to 20 do u(n):=simplify((24*sqrt(19)+105)/2*(170+39*sqrt(19))^(n)+(-24*sqrt(19)+105)/2*(170-39*sqrt(19))^(n)):od:seq(u(n),n=0..20);

%t LinearRecurrence[{340, -1}, {105, 35634}, 50] (* _G. C. Greubel_, Jun 23 2016 *)

%o (Magma) I:=[105,35634]; [n le 2 select I[n] else 340*Self(n-1)-Self(n-2): n in [1..20]]; // _Vincenzo Librandi_, Jun 25 2016

%Y Cf. A167708, A167709, A167774, A167775, A167778, A167780.

%K easy,nonn

%O 0,1

%A _Richard Choulet_, Nov 11 2009