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%I #16 Sep 08 2022 08:45:48
%S 220,74801,25432120,8646845999,2939902207540,999558103717601,
%T 339846815361776800,115546917664900394399,39285612159250772318860,
%U 13356992587227597688018001,4541338194045223963153801480
%N Subsequence of A167709 whose indices are congruent to 4 mod 5, i.e., a(n) = A167709(5*n+4).
%H G. C. Greubel, <a href="/A167825/b167825.txt">Table of n, a(n) for n = 0..100</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*(w(n))^2 + 81).
%F G.f.: (220 + x)/(1 - 340*x + x^2).
%F a(n) = ((959*sqrt(19) + 4180)/38)*(170 + 39*sqrt(19))^n + ((-959*sqrt(19) + 4180)/38)*(170 - 39*sqrt(19))^n.
%e a(0) = A167709(4) = 220, a(1) = A167709(9) = 74801.
%p w(0):=220: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((959*sqrt(19)+4180)/38*(170+39*sqrt(19))^(n)+(-959*sqrt(19)+4180)/38*(170-39*sqrt(19))^(n)):od:seq(u(n),n=0..20);taylor(((220+74801*z-220*340*z)/(1-340*z+z^2)),z=0,21);
%t LinearRecurrence[{340, -1}, {220, 74801}, 50] (* _G. C. Greubel_, Jun 27 2016 *)
%t RecurrenceTable[{a[1] == 220, a[2] == 74801, a[n] == 340 a[n-1] - a[n-2]}, a, {n, 15}] (* _Vincenzo Librandi_, Jun 28 2016 *)
%o (Magma) I:=[220,74801]; [n le 2 select I[n] else 340*Self(n-1)-Self(n-2): n in [1..30]]; // _Vincenzo Librandi_, Jun 28 2016
%K nonn,easy
%O 0,1
%A _Richard Choulet_, Nov 13 2009
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