OFFSET
0,2
COMMENTS
LINKS
Indranil Ghosh, Table of n, a(n) for n = 0..423
Tanya Khovanova, Recursive Sequences
Index entries for linear recurrences with constant coefficients, signature (227, -1).
FORMULA
a(n) = S(n, 227) = U(n, 227/2) = S(2*n+1, sqrt(229))/sqrt(229) 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) = 227*a(n-1)-a(n-2), n >= 1; a(0)=1, a(1)=227; a(-1):=0.
a(n) = (ap^(n+1) - am^(n+1))/(ap-am) with ap := (227+15*sqrt(229))/2 and am := (227-15*sqrt(229))/2 = 1/ap.
G.f.: 1/(1-227*x+x^2).
MATHEMATICA
CoefficientList[Series[1/(1 - 227*x + x^2), {x, 0, 15}], x] (* Wesley Ivan Hurt, Feb 09 2017 *)
LinearRecurrence[{227, -1}, {1, 227}, 20] (* Harvey P. Dale, Jan 15 2019 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Wolfdieter Lang, Sep 10 2004
STATUS
approved