A190871 a(n) = 11*a(n-1) - 11*a(n-2), a(0)=0, a(1)=1.

0, 1, 11, 110, 1089, 10769, 106480, 1052821, 10409751, 102926230, 1017681269, 10062305429, 99490865760, 983714163641, 9726456276691, 96170163243550, 950880776635449, 9401816747310889, 92960295677429840, 919143268231308461, 9088012698092664831

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 (11,-11).

Crossrefs

Cf. A057086, A190872, A190873.

Programs

Magma

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

Mathematica

LinearRecurrence[{11,-11}, {0,1}, 50] (* T. D. Noe, May 23 2011 *)

PARI

concat(0, Vec(x/(1-11*x+11*x^2) + O(x^100))) \\ Altug Alkan, Dec 18 2015

SageMath

def A190871(n): return (sqrt(11))^(n-1)*chebyshev_U(n-1, sqrt(11)/2)
[A190871(n) for n in range(31)] # G. C. Greubel, Sep 11 2023

Formula

a(n) = ((11+sqrt(77))^n-(11-sqrt(77))^n)/(2^n*sqrt(77)).

G.f.: x/(1-11x+11x^2). - Philippe Deléham, Dec 21 2011

E.g.f.: (2/sqrt(77))*exp(11*x/2)*sinh(sqrt(77)*x/2). - G. C. Greubel, Dec 18 2015

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

Extensions

Extended by T. D. Noe, May 23 2011