A164039 a(n+1) = 3*a(n) - n.

1, 2, 4, 9, 23, 64, 186, 551, 1645, 4926, 14768, 44293, 132867, 398588, 1195750, 3587235, 10761689, 32285050, 96855132, 290565377, 871696111, 2615088312, 7845264914, 23535794719, 70607384133, 211822152374, 635466457096

Offset: 0

Author

Rolf Pleisch, Aug 08 2009

Keywords

• nonn
• easy

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (5,-7,3).

Programs

Mathematica

Transpose[NestList[Flatten[{Rest[#],ListCorrelate[#,{3,-7,5}]}]&, {1,2,4},30]][[1]] (* Harvey P. Dale, Mar 24 2011 *)
Table[(3^n + 2*n + 3)/4, {n,0,50}] (* G. C. Greubel, Sep 08 2017 *)

PARI

x='x+O('x^50); Vec((1-3*x+x^2)/((1-3*x)*(1-x)^2)) \\ G. C. Greubel, Sep 08 2017

Formula

a(0) = 1; a(n+1) = 3*a(n) - n.

a(n) = (3^n + 2*n + 3)/4.

From R. J. Mathar, Aug 09 2009: (Start)

a(n) = 5*a(n-1)-7*a(n-2)+3*a(n-3).

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

E.g.f.: (1/4)*((2*x + 3)*exp(x) + exp(3*x)). - G. C. Greubel, Sep 08 2017