OFFSET
0,4
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (9,-19,3).
FORMULA
a(n) = ( (3+sqrt(8))^n + (3-sqrt(8))^n - 2*3^n )/16.
E.g.f.: (1/4)*exp(3*x)*( sinh(sqrt(2)*x) )^2.
G.f.: x^2 / ( (1-3*x)*(1-6*x+x^2) ). - R. J. Mathar, Sep 27 2012
a(n) = (A001541(n) - 3^n)/8. - R. J. Mathar, Sep 27 2012
MATHEMATICA
LinearRecurrence[{9, -19, 3}, {0, 0, 1}, 30] (* Harvey P. Dale, Jun 06 2021 *)
PROG
(Magma) [(Evaluate(ChebyshevFirst(n), 2) -3^n)/8: n in [0..40]]; // G. C. Greubel, Oct 11 2022
(SageMath) [(chebyshev_T(n, 3) - 3^n)/8 for n in range(41)] # G. C. Greubel, Oct 11 2022
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Paul Barry, May 16 2003
STATUS
approved