A190870 a(n) = 11*a(n-1) - 22*a(n-2), a(0)=0, a(1)=1.

0, 1, 11, 99, 847, 7139, 59895, 501787, 4201967, 35182323, 294562279, 2466173963, 20647543455, 172867150819, 1447292702999, 12117142414971, 101448127098703, 849352264956371, 7111016118348615, 59535427472794603, 498447347597071103, 4173141419166300867

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, -22).

Crossrefs

Cf. A190871, A190872, A190873

Programs

Mathematica

LinearRecurrence[{11, -22}, {0, 1}, 50] (* T. D. Noe, May 23 2011 *)

PARI

concat(0, Vec(x/(1-11*x+22*x^2) + O(x^100))) \\ Altug Alkan, Dec 18 2015

Formula

a(n) = ((11+sqrt(33))^n-(11-sqrt(33))^n)/(2^n*sqrt(33)).

E.g.f.: (2/sqrt(33))*exp(11*x/2)*sinh(sqrt(33)*x/2). - G. C. Greubel, Dec 18 2015

G.f.: x/(1-11*x+22*x^2). - G. C. Greubel, Dec 18 2015

Extensions

Extended by T. D. Noe, May 23 2011