OFFSET
0,2
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (6,-3).
FORMULA
a(n) = ((3+2*sqrt(6))*(3+sqrt(6))^n + (3-2*sqrt(6))*(3-sqrt(6))^n)/6.
G.f.: (1+x)/(1-6*x+3*x^2).
a(n) = 3^((n-1)/2)*(sqrt(3)*ChebyshevU(n, sqrt(3)) + ChebyshevU(n-1, sqrt(3))). - G. C. Greubel, Jul 16 2021
MATHEMATICA
LinearRecurrence[{6, -3}, {1, 7}, 31] (* G. C. Greubel, Jul 16 2021 *)
PROG
(Magma) [ n le 2 select 6*n-5 else 6*Self(n-1)-3*Self(n-2): n in [1..21] ];
(Sage) [3^((n-1)/2)*(sqrt(3)*chebyshev_U(n, sqrt(3)) + chebyshev_U(n-1, sqrt(3))) for n in (0..30)] # G. C. Greubel, Jul 16 2021
CROSSREFS
KEYWORD
nonn
AUTHOR
Klaus Brockhaus, Aug 15 2009
STATUS
approved