A153465 a(n) = 9*4^n - 2.

34, 142, 574, 2302, 9214, 36862, 147454, 589822, 2359294, 9437182, 37748734, 150994942, 603979774, 2415919102, 9663676414, 38654705662, 154618822654, 618475290622, 2473901162494, 9895604649982, 39582418599934, 158329674399742, 633318697598974, 2533274790395902

Offset: 1

Author

Vincenzo Librandi, Dec 27 2008

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (5,-4).

Crossrefs

Cf. A002063.

Programs

Magma

I:=[34, 142]; [n le 2 select I[n] else 5*Self(n-1)-4*Self(n-2): n in [1..50]]; // Vincenzo Librandi, Feb 22 2012

Mathematica

LinearRecurrence[{5, -4}, {34, 142}, 50] (* Vincenzo Librandi, Feb 22 2012 *)
CoefficientList[Series[(34 - 28 x )/((1 - x) (1 - 4 x)), {x, 0, 30}], x] (* Vincenzo Librandi, May 03 2014 *)

PARI

a(n)=9*4^n-2; \\ Charles R Greathouse IV, Jan 11 2012

Formula

a(n) = A002063(n) - 2. - R. J. Mathar, Jan 03 2009

a(n) = 5*a(n-1) - 4*a(n-2).

G.f.: x*(34-28*x)/((1-x)*(1-4*x)). - Vincenzo Librandi, May 03 2014

E.g.f.: 9*exp(4*x) - 2*exp(x) - 7. - Stefano Spezia, Sep 14 2024