A190963 a(n) = 3*a(n-1) - 9*a(n-2), with a(0)=0, a(1)=1.

0, 1, 3, 0, -27, -81, 0, 729, 2187, 0, -19683, -59049, 0, 531441, 1594323, 0, -14348907, -43046721, 0, 387420489, 1162261467, 0, -10460353203, -31381059609, 0, 282429536481, 847288609443, 0, -7625597484987, -22876792454961, 0, 205891132094649

Offset: 0

Author

Vladimir Joseph Stephan Orlovsky, May 24 2011

Keywords

• sign
• easy

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (3,-9).

Crossrefs

Cf. A190958 (index to generalized Fibonacci sequences).

Cf. A128834.

Programs

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

Mathematica

LinearRecurrence[{3,-9}, {0,1}, 50]

PARI

my(x='x+O('x^30)); concat([0], Vec(x/(1-3*x+9*x^2))) \\ 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

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)