A145563 a(0)=0 and a(n+1) = 3*a(n) + 2^(n+2).

0, 4, 20, 76, 260, 844, 2660, 8236, 25220, 76684, 232100, 700396, 2109380, 6344524, 19066340, 57264556, 171924740, 516036364, 1548633380, 4646948716, 13942943300, 41833024204, 125507461220, 376539160876, 1129651037060, 3389020220044, 10167194877860

Offset: 0

Author

N. J. A. Sloane, Mar 18 2009

Keywords

• nonn

Comments

Suggested by a discussion on the Sequence Fans Mailing List; the formula is due to Andrew V. Sutherland.

First differences of A255459. - Klaus Purath, Apr 25 2020

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..170
• Index entries for linear recurrences with constant coefficients, signature (5,-6).

Crossrefs

Cf. A001047, A056182, A210448, A217764, A245804.

Programs

Magma

[ 4*(3^n - 2^n): n in [0..50]]; // Vincenzo Librandi, Apr 24 2011

Mathematica

CoefficientList[Series[4x/((1-2x)(1-3x)),{x,0,40}],x] (* or *) RecurrenceTable[{a[0]==0, a[n]==(3a[n-1]+2^(n+1))},a,{n,40}] (* Harvey P. Dale, Apr 24 2011 *)

PARI

a(n) = 4*(3^n - 2^n) \\ Felix Fröhlich, Sep 01 2018

Formula

From R. J. Mathar, Mar 18 2009: (Start)

a(n) = 4*(3^n - 2^n) = 4*A001047(n).

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

a(n) = A056182(n)*2. - Omar E. Pol, Mar 18 2009

a(n) = A217764(n,7). - Ross La Haye, Mar 27 2013

From Klaus Purath, Apr 25 2020: (Start)

a(n) = 5*a(n-1) - 6*a(n-2).

a(n) = 2*A210448(n) - A056182(n).

a(n) = (A056182(n) + A245804(n+1))/2. (End)