A099158 a(n) = 5^(n-1) * U(n-1, 7/5) where U is the Chebyshev polynomial of the second kind.

0, 1, 14, 171, 2044, 24341, 289674, 3446911, 41014904, 488035881, 5807129734, 69098919251, 822206626164, 9783419785021, 116412711336194, 1385192464081191, 16482376713731824, 196123462390215761

Offset: 0

Author

Paul Barry, Oct 01 2004

Keywords

• easy
• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..925
• Index entries for sequences related to Chebyshev polynomials.
• Index entries for linear recurrences with constant coefficients, signature (14,-25).

Crossrefs

Cf. A099141, A099157.

Programs

Magma

[n le 2 select n-1 else 14*Self(n-1) -25*Self(n-2): n in [1..30]]; // G. C. Greubel, Jul 20 2023

Mathematica

LinearRecurrence[{14,-25}, {0,1}, 40] (* G. C. Greubel, Jul 20 2023 *)

PARI

a(n) = 5^(n-1)*polchebyshev(n-1, 2, 7/5); \\ Michel Marcus, Sep 08 2019

SageMath

A099158=BinaryRecurrenceSequence(14,-25,0,1)
[A099158(n) for n in range(41)] # G. C. Greubel, Jul 20 2023

Formula

G.f.: x/(1 - 14*x + 25*x^2).

E.g.f.: exp(7*x)*sinh(2*sqrt(6)*x)/sqrt(6).

a(n) = 14*a(n-1) - 25*a(n-2).

a(n) = sqrt(6)*(sqrt(6)+1)^(2*n)/24 - sqrt(6)*(sqrt(6)-1)^(2*n)/24.

a(n) = Sum_{k=0..n} binomial(2n, 2k+1)*6^k/2.

a(n) = 5^(n-1)*U(n-1, 7/5), where U is the Chebyshev polynomial of the second kind.