A168617 a(n) = 7*2^(n-1) - 2*n - 5.

0, 5, 17, 43, 97, 207, 429, 875, 1769, 3559, 7141, 14307, 28641, 57311, 114653, 229339, 458713, 917463, 1834965, 3669971, 7339985, 14680015, 29360077, 58720203, 117440457, 234880967, 469761989, 939524035, 1879048129, 3758096319

Offset

1,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (4,-5,2).

Formula

a(n) = 2*a(n-1) + 2*n + 1 (with a(1)=0).

From Colin Barker, Sep 18 2012: (Start)

a(n) = 4*a(n-1) - 5*a(n-2) + 2*a(n-3).

G.f.: x^2*(5 - 3*x)/(1 - 4*x + 5*x^2 - 2*x^3). (End)

E.g.f.: (1/2)*(3 - (10 + 4*x)*exp(x) + 7*exp(2*x)). - G. C. Greubel, Jul 27 2016

Mathematica

Table[(7*2^(n-1) - 2*n - 5), {n, 1, 40}] (* Vincenzo Librandi, Sep 18 2012  *)
LinearRecurrence[{4, -5, 2}, {0, 5, 17}, 25] (* G. C. Greubel, Jul 27 2016 *)

Prog

(Magma) I:=[0, 5, 17]; [n le 3 select I[n] else 4*Self(n-1)-5*Self(n-2)+2*Self(n-3): n in [1..30]]; // Vincenzo Librandi, Sep 18 2012

Crossrefs

Sequence in context: A146640 A100705 A100662 * A046916 A089527 A146778

Adjacent sequences: A168614 A168615 A168616 * A168618 A168619 A168620

Keyword

nonn,easy

Author

Vincenzo Librandi, Dec 01 2009

Extensions

Definition and examples simplified by Jon E. Schoenfield, Jun 19 2010

Status

approved