A164044 a(n+1) = 4*a(n) - n.

1, 3, 10, 37, 144, 571, 2278, 9105, 36412, 145639, 582546, 2330173, 9320680, 37282707, 149130814, 596523241, 2386092948, 9544371775, 38177487082, 152709948309, 610839793216, 2443359172843, 9773436691350, 39093746765377

Offset: 0

Author

Rolf Pleisch, Aug 08 2009

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (6, -9, 4).

Programs

Mathematica

Table[(5*4^n + 3*n + 4)/9, {n,0,50}] (* G. C. Greubel, Sep 08 2017 *)

PARI

x='x+O('x^50); Vec((1-3*x+x^2)/((1-4*x)*(1-x)^2)) \\ G. C. Greubel, Sep 08 2017

Formula

a(0)=1; a(n+1) = 4*a(n) - n.

a(n) = (5*4^n + 3*n + 4)/9.

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

a(n) = 6*a(n-1) - 9*a(n-2) + 4*a(n-3).

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

E.g.f.: (1/9)*(5*exp(4*x) + (3*x + 4)*exp(x)). - G. C. Greubel, Sep 08 2017