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Subsequence of A167708 whose indices are congruent to 1 mod 5, i.e., a(n) = A167708(5n+1).
7

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

%S 10,2441,829930,282173759,95938248130,32618722190441,

%T 11090269606501810,3770659047488424959,1282012985876457984250,

%U 435880644538948226220041,148198137130256520456829690,50386930743642678007095874559,17131408254701380265892140520370

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

%H G. C. Greubel, <a href="/A167775/b167775.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.: (10 + 2441*z - 10*z*340)/(1 - 340*z + z^2).

%F a(n) = ((10 + sqrt(19))/2)*(170 + 39*sqrt(19))^(n) + ((10 - sqrt(19))/2)* (170 - 39*sqrt(19))^(n).

%e a(0) = A167708(1) = 10, a(1) = A167708(6) = 2441, ...

%p u(0):=10:u(1):=2441:for n from 0 to 20 do u(n+2):=340*u(n+1)-u(n):od:seq(u(n),n=0..20); taylor(((10+2441*z-10*z*340)/(1-340*z+z^2)),z=0,20);

%t LinearRecurrence[{340, -1}, {10, 2441}, 50] (* _G. C. Greubel_, Jun 23 2016 *)

%o (Magma) I:=[10,2441]; [n le 2 select I[n] else 340*Self(n-1)-Self(n-2): n in [1..20]]; // _Vincenzo Librandi_, Jun 24 2016

%Y Cf. A167708, A167709, A167774, A167778, A167779, A167780.

%K easy,nonn

%O 0,1

%A _Richard Choulet_, Nov 11 2009