OFFSET
0,2
COMMENTS
LINKS
Indranil Ghosh, Table of n, a(n) for n = 0..446
Hacène Belbachir, Soumeya Merwa Tebtoub, and László Németh, Ellipse Chains and Associated Sequences, J. Int. Seq., Vol. 23 (2020), Article 20.8.5.
Tanya Khovanova, Recursive Sequences
Index entries for linear recurrences with constant coefficients, signature (171,-1).
FORMULA
a(n) = S(n, 171) = U(n, 171/2) = S(2*n+1, sqrt(173))/sqrt(173) with S(n, x) = U(n, x/2) Chebyshev's polynomials of the second kind, A049310. S(-1, x) = 0 = U(-1, x).
a(n) = 171*a(n-1) - a(n-2), n >= 1, a(-1)=0, a(0)=1, a(1)=171.
a(n) = (ap^(n+1) - am^(n+1))/(ap-am) with ap = (171+13*sqrt(173))/2 and am = (171-13*sqrt(173))/2 = 1/ap.
G.f.: 1/(1-171*x+x^2).
MATHEMATICA
CoefficientList[Series[1/(1-171x+x^2), {x, 0, 30}], x] (* or *) LinearRecurrence[{171, -1}, {1, 171}, 30] (* Harvey P. Dale, Mar 21 2013 *)
PROG
(PARI) my(x='x+O('x^30)); Vec(1/(1-171*x+x^2)) \\ G. C. Greubel, Jan 14 2019
(Magma) m:=30; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!( 1/(1-171*x+x^2) )); // G. C. Greubel, Jan 14 2019
(Sage) (1/(1-171*x+x^2)).series(x, 30).coefficients(x, sparse=False) # G. C. Greubel, Jan 14 2019
(GAP) a:=[1, 171];; for n in [3..30] do a[n]:=171*a[n-1]-a[n-2]; od; a; # G. C. Greubel, Jan 14 2019
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Wolfdieter Lang, Sep 10 2004
STATUS
approved