A190976 a(n) = 8*a(n-1) - 3*a(n-2), with a(0)=0, a(1)=1.

0, 1, 8, 61, 464, 3529, 26840, 204133, 1552544, 11807953, 89805992, 683024077, 5194774640, 39509124889, 300488675192, 2285382026869, 17381590189376, 132196575434401, 1005427832907080, 7646832936953437, 58158379996906256, 442326541164389737

Offset

0,3

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (8,-3).

Formula

a(n) = ((4 + sqrt(13))^n - (4 - sqrt(13))^n)/(2*sqrt(13)). - Giorgio Balzarotti, May 28 2011

G.f.: x/(1 - 8*x + 3*x^2). - Philippe Deléham, Oct 12 2011

From G. C. Greubel, Jun 11 2022: (Start)

a(n) = 3^((n-1)/2)*ChebyshevU(n-1, 4/sqrt(3)).

E.g.f.: (1/sqrt(13))*exp(4*x)*sinh(sqrt(13)*x). (End)

Mathematica

LinearRecurrence[{8, -3}, {0, 1}, 50]

Prog

(Magma) [n le 2 select n-1 else 8*Self(n-1) - 3*Self(n-2): n in [1..51]]; // G. C. Greubel, Jun 11 2022
(SageMath) [lucas_number1(n, 8, 3) for n in (0..50)] # G. C. Greubel, Jun 11 2022

Crossrefs

Cf. A190958 (index to generalized Fibonacci sequences).

Sequence in context: A283410 A081907 A278596 * A254602 A363571 A361772

Adjacent sequences: A190973 A190974 A190975 * A190977 A190978 A190979

Keyword

nonn,easy

Author

Vladimir Joseph Stephan Orlovsky, May 24 2011

Status

approved