A051667 a(n) = 6*2^n - 4*n - 6.

0, 2, 10, 30, 74, 166, 354, 734, 1498, 3030, 6098, 12238, 24522, 49094, 98242, 196542, 393146, 786358, 1572786, 3145646, 6291370, 12582822, 25165730, 50331550, 100663194, 201326486, 402653074, 805306254, 1610612618, 3221225350, 6442450818, 12884901758, 25769803642

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

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

Formula

From Colin Barker, Jun 24 2012: (Start)

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

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

E.g.f.: 2*exp(x)*(3*exp(x) - 2*x - 3). - Stefano Spezia, May 15 2023

Mathematica

CoefficientList[Series[2 x (1 + x)/((1 - x)^2 (1 - 2 x)), {x, 0, 40}], x] (* Vincenzo Librandi, Jul 05 2012 *)

Prog

(Magma) I:=[0, 2, 10]; [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, Jul 04 2012

Crossrefs

Row sums of A051666.

Equals 2 * A050488.

Cf. A000290.

Sequence in context: A167214 A034827 A328532 * A106355 A120546 A058966

Adjacent sequences: A051664 A051665 A051666 * A051668 A051669 A051670

Keyword

nonn,easy

Author

Asher Auel

Status

approved