A167823 - OEIS

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

%S 15,5124,1742145,592324176,201388477695,68471490092124,

%T 23280105242844465,7915167311077025976,2691133605660945987375,

%U 914977510757410558681524,311089662523913929005730785,105769570280619978451389785376,35961342805748268759543521297055

%N Subsequence of A167709 whose indices are congruent to 2 mod 5, i.e., a(n) = A167709(5*n+2).

%H G. C. Greubel, <a href="/A167823/b167823.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*(a(n))^2 + 81).

%F G.f.: (15 + 24*z)/(1 - 340*z + z^2).

%F a(n) = (66*sqrt(19) + 285)/38*(170 + 39*sqrt(19))^n + (-66*sqrt(19) + 285)/38*(170 - 39*sqrt(19))^n.

%e a(0) = A167709(2) = 15, a(1) = A167709(7) = 5124.

%p w(0):=15: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((66*sqrt(19)+285)/38*(170+39*sqrt(19))^(n)+(-66*sqrt(19)+285)/38*(170-39*sqrt(19))^(n)):od:seq(u(n),n=0..20);taylor(((15+5124*z-15*340*z)/(1-340*z+z^2)),z=0,21);

%t LinearRecurrence[{340,-1},{15, 5124}, 50] (* _G. C. Greubel_, Jun 27 2016 *)

%t RecurrenceTable[{a[1] == 15, a[2] == 5124, a[n] == 340 a[n-1] - a[n-2]}, a, {n, 15}] (* _Vincenzo Librandi_, Jun 28 2016 *)

%o (Magma) I:=[15,5124]; [n le 2 select I[n] else 340*Self(n-1)-Self(n-2): n in [1..30]]; // _Vincenzo Librandi_, Jun 28 2016

%K easy,nonn

%O 0,1

%A _Richard Choulet_, Nov 13 2009