A190873 a(n) = 12*a(n-1) - 12*a(n-2), a(0)=0, a(1)=1.

0, 1, 12, 132, 1440, 15696, 171072, 1864512, 20321280, 221481216, 2413919232, 26309256192, 286744043520, 3125217447936, 34061680852992, 371237560860672, 4046110560092160, 44098475990777856, 480628385168228352, 5238358910129405952, 57092766299534131200

Offset: 0

Author

Rolf Pleisch, May 22 2011

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (12,-12).

Crossrefs

Cf. A057086, A190871, A190872.

Programs

Magma

[n le 2 select n-1 else 12*(Self(n-1) - Self(n-2)): n in [1..31]]; // G. C. Greubel, Sep 11 2023

Mathematica

LinearRecurrence[{12,-12}, {0,1}, 50] (* T. D. Noe, May 23 2011 *)

PARI

concat(0, Vec(x/(1-12*x+12*x^2) + O(x^100))) \\ Altug Alkan, Dec 18 2015

SageMath

def A190873(n): return (2*sqrt(3))^(n-1)*chebyshev_U(n-1, sqrt(3))
[A190873(n) for n in range(31)] # G. C. Greubel, Sep 11 2023

Formula

a(n) = 2^(n-2)*((3+sqrt(6))^n - (3-sqrt(6))^n)/sqrt(6).

G.f.: x/(1 - 12*x + 12*x^2). - Philippe Deléham, Dec 21 2011

E.g.f.: (1/(2*sqrt(6)))*exp(6*x)*sinh(2*sqrt(6)*x). - G. C. Greubel, Dec 18 2015

a(n) = (2*sqrt(3))^(n-1)*chebyshev_U(n-1, sqrt(3)). - G. C. Greubel, Sep 11 2023

Extensions

Extended by T. D. Noe, May 23 2011