OFFSET
0,1
COMMENTS
LINKS
FORMULA
a(n) = 57*S(n-1,6) - 11*S(n-2,6) with the Chebyshev polynomials S(n, 6) = A001109(n+1), n >= -1, with S(-2, 6) = -1.
O.g.f.: (11 - 9*x)/(1 - 6*x + x^2).
a(n) = 6*a(n-1) - a(n-2), n >= 1, with a(-1) = 9 and a(0) = 11.
a(n) = (((3-2*sqrt(2))^n*(-12+11*sqrt(2))+(3+2*sqrt(2))^n*(12+11*sqrt(2)))) / (2*sqrt(2)). - Colin Barker, Sep 28 2016
MATHEMATICA
LinearRecurrence[{6, -1}, {11, 57}, 30] (* Harvey P. Dale, Sep 01 2022 *)
PROG
(PARI) a(n) = round((((3-2*sqrt(2))^n*(-12+11*sqrt(2))+(3+2*sqrt(2))^n*(12+11*sqrt(2)))) / (2*sqrt(2))) \\ Colin Barker, Sep 28 2016
(PARI) Vec((11-9*x)/(1-6*x+x^2) + O(x^30)) \\ Colin Barker, Oct 09 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Wolfdieter Lang, Sep 27 2016
STATUS
approved