A164550 a(n) = 6*a(n-1) - 3*a(n-2) for n > 1; a(0) = 1, a(1) = 7.

1, 7, 39, 213, 1161, 6327, 34479, 187893, 1023921, 5579847, 30407319, 165704373, 903004281, 4920912567, 26816462559, 146136037653, 796366838241, 4339792916487, 23649656984199, 128878563155733, 702322407981801

Offset

0,2

Comments

Binomial transform of A164549.

Inverse binomial transform of A154235.

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

Cf. A154235, A164549.

Sequence in context: A246987 A322876 A092923 * A125786 A287809 A155589

Adjacent sequences: A164547 A164548 A164549 * A164551 A164552 A164553

Keyword

nonn

Author

Klaus Brockhaus, Aug 15 2009

Status

approved