A167823 Subsequence of A167709 whose indices are congruent to 2 mod 5, i.e., a(n) = A167709(5*n+2).
15, 5124, 1742145, 592324176, 201388477695, 68471490092124, 23280105242844465, 7915167311077025976, 2691133605660945987375, 914977510757410558681524, 311089662523913929005730785, 105769570280619978451389785376, 35961342805748268759543521297055
Offset: 0
Examples
a(0) = A167709(2) = 15, a(1) = A167709(7) = 5124.
Links
- G. C. Greubel, Table of n, a(n) for n = 0..100
- Index entries for linear recurrences with constant coefficients, signature (340,-1).
Programs
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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
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Maple
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);
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Mathematica
LinearRecurrence[{340,-1},{15, 5124}, 50] (* G. C. Greubel, Jun 27 2016 *) RecurrenceTable[{a[1] == 15, a[2] == 5124, a[n] == 340 a[n-1] - a[n-2]}, a, {n, 15}] (* Vincenzo Librandi, Jun 28 2016 *)
Formula
a(n+2) = 340*a(n+1) - a(n).
a(n+1) = 170*a(n) + 39*sqrt(19*(a(n))^2 + 81).
G.f.: (15 + 24*z)/(1 - 340*z + z^2).
a(n) = (66*sqrt(19) + 285)/38*(170 + 39*sqrt(19))^n + (-66*sqrt(19) + 285)/38*(170 - 39*sqrt(19))^n.