OFFSET
0,3
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (3,-9).
FORMULA
G.f.: x/(1-3*x+9*x^2). - Philippe Deléham, Oct 11 2011
From G. C. Greubel, Jan 11 2024: (Start)
a(n) = 3^(n-1)*ChebyshevU(n-1, 1/2).
a(n) = 3^(n-1)*A128834(n).
E.g.f.: (2/(3*sqrt(3)))*exp(3*x/2)*sin(3*sqrt(3)*x/2). (End)
MATHEMATICA
LinearRecurrence[{3, -9}, {0, 1}, 50]
PROG
(PARI) my(x='x+O('x^30)); concat([0], Vec(x/(1-3*x+9*x^2))) \\ G. C. Greubel, Jan 25 2018
(Magma) [n le 2 select n-1 else 3*Self(n-1)-9*Self(n-2): n in [1..30]]; // G. C. Greubel, Jan 25 2018
(SageMath)
A190963=BinaryRecurrenceSequence(3, -9, 0, 1)
[A190963(n) for n in range(41)] # G. C. Greubel, Jan 11 2024
CROSSREFS
KEYWORD
sign,easy
AUTHOR
Vladimir Joseph Stephan Orlovsky, May 24 2011
STATUS
approved