A190977 a(n) = 8*a(n-1) - 5*a(n-2), with a(0)=0, a(1)=1.

0, 1, 8, 59, 432, 3161, 23128, 169219, 1238112, 9058801, 66279848, 484944779, 3548158992, 25960548041, 189943589368, 1389745974739, 10168249851072, 74397268934881, 544336902223688, 3982708873115099, 29139986473802352, 213206347424843321, 1559950847029734808

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,-5).

Formula

a(n) = ((4 + sqrt(11))^n - (4 - sqrt(11))^n)/(2*sqrt(11)). - Giorgio Balzarotti, May 28 2011

G.f.: x/(1 - 8*x + 5*x^2). - Philippe Deléham, Oct 12 2011

From G. C. Greubel, Jun 17 2022: (Start)

a(n) = 5^((n-1)/2)*ChebyshevU(n-1, 4/sqrt(5)).

E.g.f.: (1/sqrt(11))*exp(4*x)*sinh(sqrt(11)*x). (End)

Mathematica

LinearRecurrence[{8, -5}, {0, 1}, 50]

Prog

(Magma) [n le 2 select n-1 else 8*Self(n-1) -5*Self(n-2): n in [1..41]]; // G. C. Greubel, Jun 17 2022
(SageMath) [sum( (-1)^k*binomial(n-k-1, k)*5^k*8^(n-2*k-1) for k in (0..((n-1)//2))) for n in (0..40)] # G. C. Greubel, Jun 17 2022

Crossrefs

Cf. A190958 (index to generalized Fibonacci sequences).

Sequence in context: A263503 A343089 A112424 * A254662 A186362 A285231

Adjacent sequences: A190974 A190975 A190976 * A190978 A190979 A190980

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, May 24 2011

Status

approved