OFFSET
1,1
COMMENTS
lim_{n -> infinity} a(n)/a(n-1) = 17+12*sqrt(2).
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..600
Index entries for linear recurrences with constant coefficients, signature (35,-35,1).
FORMULA
a(n) = (1058 + (627 - 238*sqrt(2))*(17 + 12*sqrt(2))^n + (627 + 238*sqrt(2))*(17 - 12*sqrt(2))^n)/8.
G.f.: x*(1369 -5890*x +289*x^2)/((1-x)*(1-34*x+x^2)).
a(n) = -289*[n=0] + (529/4) + (3/4)*(209*ChebyshevU(n, 17) - 5457*ChebyshevU(n - 1, 17)). - G. C. Greubel, Jan 04 2022
EXAMPLE
a(3) = 34*a(2) - a(1) - 4232 = 34*42025 - 1369 - 4232 = 1423249.
MATHEMATICA
LinearRecurrence[{35, -35, 1}, {1369, 42025, 1423249}, 30] (* G. C. Greubel, Jan 04 2022 *)
PROG
(PARI) {m=14; v=concat([1369, 42025], vector(m-2)); for(n=3, m, v[n]=34*v[n-1]-v[n-2]-4232); v}
(Sage)
def a(n): return -289*bool(n==0) + (529/4) + (3/4)*(209*chebyshev_U(n, 17) - 5457*chebyshev_U(n-1, 17))
[a(n) for n in (1..30)] # G. C. Greubel, Jan 04 2022
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Klaus Brockhaus, Feb 11 2009
EXTENSIONS
Revised by Klaus Brockhaus, Feb 16 2009
G.f. corrected by Klaus Brockhaus, Sep 22 2009
STATUS
approved