login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

A167774
Subsequence of A167708 whose indices are congruent to 1 mod 5, i.e., a(n) = A167708(5*n+1).
8
9, 1530, 520191, 176863410, 60133039209, 20445056467650, 6951259065961791, 2363407637370541290, 803551645446918076809, 273205196044314775573770, 92888963103421576777004991, 31581974249967291789406123170, 10737778356025775786821304872809
OFFSET
0,1
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
EXAMPLE
a(0)=A167708(1)=9, a(1)=A167708(6)=1530.
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);
MATHEMATICA
LinearRecurrence[{340, -1}, {9, 1530}, 50] (* G. C. Greubel, Jun 23 2016 *)
PROG
(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
KEYWORD
easy,nonn
AUTHOR
Richard Choulet, Nov 11 2009
STATUS
approved