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

0,3

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).

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.

Mathematica

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

Prog

(PARI) a(n) = 5^(n-1)*polchebyshev(n-1, 2, 7/5); \\ Michel Marcus, Sep 08 2019
(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
(SageMath)
A099158=BinaryRecurrenceSequence(14, -25, 0, 1)
[A099158(n) for n in range(41)] # G. C. Greubel, Jul 20 2023

Crossrefs

Cf. A099141, A099157.

Sequence in context: A098299 A341500 A254811 * A014882 A048443 A191690

Adjacent sequences: A099155 A099156 A099157 * A099159 A099160 A099161

Keyword

easy,nonn

Author

Paul Barry, Oct 01 2004

Status

approved