A163066 a(n) = 12*a(n-1) - 31*a(n-2) for n > 1; a(0) = 2, a(1) = 17.

2, 17, 142, 1177, 9722, 80177, 660742, 5443417, 44838002, 369310097, 3041743102, 25052304217, 206333614442, 1699381942577, 13996241263222, 115274054938777, 949405180105442, 7819366458163217, 64400836914689902, 530409682773219097

Offset: 0

Author

Klaus Brockhaus, Jul 20 2009

Keywords

• nonn

Comments

Binomial transform of A162773. Inverse binomial transform of A163067.

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (12,-31).

Crossrefs

Cf. A162773, A163067.

Programs

Magma

[ n le 2 select 15*n-13 else 12*Self(n-1)-31*Self(n-2): n in [1..20] ];

Mathematica

CoefficientList[Series[(2-7*x)/(1-12*x+31*x^2), {x,0,50}],x] (* or *) LinearRecurrence[{12,-31}, {2,17}, 30] (* G. C. Greubel, Dec 22 2017 *)

PARI

x='x+O('x^30); Vec((2-7*x)/(1-12*x+31*x^2)) \\ G. C. Greubel, Dec 22 2017

Formula

a(n) = ((2+sqrt(5))*(6+sqrt(5))^n + (2-sqrt(5))*(6-sqrt(5))^n)/2.

G.f.: (2-7*x)/(1-12*x+31*x^2).