OFFSET
0,2
LINKS
Harvey P. Dale, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (6,3).
FORMULA
a(n) = 3*abs(A099842(n-1)), for n > 0.
G.f.: (1-3*x)/(1-6*x-3*x^2). - Philippe Deléham, Mar 03 2012
a(n) = 6*a(n-1) + 3*a(n-2), a(0) = 1, a(1) = 3. - Philippe Deléham, Mar 03 2012
a(n) = Sum_{k=0..n} A201701(n,k)*3^(n-k). - Philippe Deléham, Mar 03 2012
G.f.: G(0)/2, where G(k) = 1 + 1/(1 - x*(4*k-3)/(x*(4*k+1) - 1/G(k+1))); (continued fraction). - Sergei N. Gladkovskii, May 27 2013
a(n) = (-i*sqrt(3))^n * ChebyshevT(n, i*sqrt(3)). - G. C. Greubel, Oct 10 2022
MATHEMATICA
a[n_]= ((3+2*Sqrt[3])^n + (3-2*Sqrt[3])^n)/2; Table[FullSimplify[a[n]], {n, 0, 30}]
LinearRecurrence[{6, 3}, {1, 3}, 30] (* Harvey P. Dale, Aug 25 2014 *)
PROG
(Magma) [n le 2 select 3^(n-1) else 6*Self(n-1) +3*Self(n-2): n in [1..31]]; // G. C. Greubel, Oct 10 2022
(SageMath)
A141041 = BinaryRecurrenceSequence(6, 3, 1, 3)
[A141041(n) for n in range(31)] # G. C. Greubel, Oct 10 2022
CROSSREFS
KEYWORD
nonn
AUTHOR
Roger L. Bagula, Aug 18 2008
EXTENSIONS
Edited by N. J. A. Sloane, Aug 24 2008
STATUS
approved