A190964 a(n) = 3*a(n-1) - 10*a(n-2), with a(0)=0, a(1)=1.

0, 1, 3, -1, -33, -89, 63, 1079, 2607, -2969, -34977, -75241, 124047, 1124551, 2133183, -4845961, -35869713, -59149529, 181248543, 1135240919, 1593237327, -6572697209, -35650464897, -41224422601, 232831381167, 1110738369511, 1003901296863, -8095679804521

Offset: 0

Author

Vladimir Joseph Stephan Orlovsky, May 24 2011

Keywords

• sign

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (3,-10).

Crossrefs

Cf. A190958 (index to generalized Fibonacci sequences).

Programs

Magma

I:=[0,1]; [n le 2 select I[n] else 3*Self(n-1) - 10*Self(n-2): n in [1..30]]; // G. C. Greubel, Jan 25 2018

Mathematica

LinearRecurrence[{3,-10}, {0,1}, 50]

PARI

my(x='x+O('x^30)); concat([0], Vec(x/(1-3*x+10*x^2))) \\ G. C. Greubel, Jan 25 2018

SageMath

A190964=BinaryRecurrenceSequence(3,-10,0,1)
[A190964(n) for n in range(41)] # G. C. Greubel, Jan 11 2024

Formula

G.f.: x/(1-3*x+10*x^2). - Philippe Deléham, Oct 11 2011

From G. C. Greubel, Jan 11 2024: (Start)

a(n) = 10^((n-1)/2)*ChebyshevU(n-1, 3/(2*sqrt(10))).

E.g.f.: (2/sqrt(31))*exp(3*x/2)*sin(sqrt(31)*x/2). (End)