A167774 Subsequence of A167708 whose indices are congruent to 1 mod 5, i.e., a(n) = A167708(5*n+1).
9, 1530, 520191, 176863410, 60133039209, 20445056467650, 6951259065961791, 2363407637370541290, 803551645446918076809, 273205196044314775573770, 92888963103421576777004991, 31581974249967291789406123170, 10737778356025775786821304872809
Offset: 0
Examples
a(0)=A167708(1)=9, a(1)=A167708(6)=1530.
Links
- G. C. Greubel, Table of n, a(n) for n = 0..250
- Index entries for linear recurrences with constant coefficients, signature (340,-1).
Programs
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Magma
I:=[9, 1530]; [n le 2 select I[n] else 340*Self(n-1)-Self(n-2): n in [1..20]]; // Vincenzo Librandi, Jun 24 2016
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Maple
u(0):=9:for n from 0 to 20 do u(n+1):=170*u(n)+39*sqrt(19*u(n)^2-1539):od:seq(u(n),n=0..20); taylor(((9+1530*z-9*z*340)/(1-340*z+z^2)),z=0,20);
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Mathematica
LinearRecurrence[{340, -1}, {9, 1530}, 50] (* G. C. Greubel, Jun 23 2016 *)
Formula
Recurrence formulas: a(n+2) = 340*a(n+1) - a(n) or a(n+1) = 170*a(n) + 39*sqrt(19*a(n)^2 - 1539).
G.f.: (9 - 1530*z)/(1 - 340*z + z^2).
a(n) = (9/2)*(170 + 39*sqrt(19))^(n) + (9/2)*(170 - 39*sqrt(19))^(n).
a(n) = 9*A114048(n+1). - R. J. Mathar, Feb 19 2016