A084131 a(n) = 10*a(n-1) - 17*a(n-2), a(0) = 1, a(1) = 5.

1, 5, 33, 245, 1889, 14725, 115137, 901045, 7053121, 55213445, 432231393, 3383685365, 26488919969, 207366548485, 1623353845377, 12708307129525, 99486055923841, 778819338036485, 6096930429659553, 47729375549975285

Offset: 0

Author

Paul Barry, May 16 2003

Keywords

• easy
• nonn

Comments

Binomial transform of A084130.

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (10,-17).

Crossrefs

Cf. A084130.

Programs

Magma

[n le 2 select 5^(n-1) else 10*Self(n-1) -17*Self(n-2): n in [1..41]]; // G. C. Greubel, Oct 13 2022

Mathematica

LinearRecurrence[{10,-17},{1,5},20] (* Harvey P. Dale, Apr 04 2021 *)

SageMath

A084131=BinaryRecurrenceSequence(10,-17,1,5)
[A084131(n) for n in range(41)] # G. C. Greubel, Oct 13 2022

Formula

a(n) = (5+sqrt(8))^n/2 + (5-sqrt(8))^n/2.

G.f.: (1-5*x)/(1-10*x+17*x^2).

E.g.f.: exp(5*x)*cosh(sqrt(8)*x).

a(n) = 17^((n-1)/2)*( sqrt(17)*ChebyshevU(n, 5/sqrt(17)) - 5*ChebyshevU(n-1, 5/sqrt(17)) ). - G. C. Greubel, Oct 13 2022