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A167824 Subsequence of A167709 whose indices are congruent to 3 mod 5, i.e., a(n) = A167709(5*n+3).

%I A167824 #17 Sep 08 2022 08:45:48
%S A167824 24,8175,2779476,945013665,321301866624,109241689638495,
%T A167824 37141853175221676,12628120837885731345,4293523943027973435624,
%U A167824 1459785512508673082380815,496322780729005820036041476,168748285662349470139171721025
%N A167824 Subsequence of A167709 whose indices are congruent to 3 mod 5, i.e., a(n) = A167709(5*n+3).
%H A167824 G. C. Greubel, <a href="/A167824/b167824.txt">Table of n, a(n) for n = 0..100</a>
%H A167824 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (340,-1).
%F A167824 a(n+2) = 340*a(n+1) - a(n).
%F A167824 a(n+1) = 170*a(n) + 39*sqrt(19*(a(n))^2 + 81).
%F A167824 G.f.: (24 + 15*x)/(1 - 340*x + x^2).
%F A167824 a(n) = ((105*sqrt(19) + 456)/38)*(170 + 39*sqrt(19))^n + ((-105*sqrt(19) + 456)/38)*(170 - 39*sqrt(19))^n.
%e A167824 a(0) = A167709(3) = 24, a(1) = A167709(8) = 8175.
%p A167824 w(0):=24:for n from 0 to 20 do w(n+1):=170*w(n)+39*sqrt(19*(w(n))^2+81) :od: seq(w(n),n=0..20);for n from 0 to 20 do u(n):=simplify((105*sqrt(19)+456)/38*(170+39*sqrt(19))^(n)+(-105*sqrt(19)+456)/38*(170-39*sqrt(19))^(n)):od:seq(u(n),n=0..20);taylor(((24+8175*z-24*340*z)/(1-340*z+z^2)),z=0,21);
%t A167824 LinearRecurrence[{340, -1}, {24, 8175}, 50] (* _G. C. Greubel_, Jun 27 2016 *)
%t A167824 RecurrenceTable[{a[1] == 24, a[2] == 8175, a[n] == 340*a[n-1] -a[n-2]}, a, {n, 15}] (* _Vincenzo Librandi_, Jun 28 2016 *)
%o A167824 (Magma) I:=[24,8175]; [n le 2 select I[n] else 340*Self(n-1)-Self(n-2): n in [1..30]]; // _Vincenzo Librandi_, Jun 28 2016
%K A167824 nonn,easy
%O A167824 0,1
%A A167824 _Richard Choulet_, Nov 13 2009