A168571 a(n) = 25*(5^n - 1)/4.

0, 25, 150, 775, 3900, 19525, 97650, 488275, 2441400, 12207025, 61035150, 305175775, 1525878900, 7629394525, 38146972650, 190734863275, 953674316400, 4768371582025, 23841857910150, 119209289550775, 596046447753900, 2980232238769525

Offset: 0

Author

Vincenzo Librandi, Nov 30 2009

Keywords

• nonn
• easy

Comments

Partial sums of A000351, starting with A000351(2).

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (6,-5).

Programs

Magma

[25*(5^n-1)/4: n in [0..30]]; // Vincenzo Librandi, Sep 24 2014

Mathematica

CoefficientList[Series[25 x / ((1 - x) (1 - 5 x)), {x, 0, 30}], x] (* Vincenzo Librandi, Sep 24 2014 *)
LinearRecurrence[{6,-5}, {0,25}, 25] (* G. C. Greubel, Jul 26 2016 *)

PARI

a(n)=25*(5^n-1)/4 \\ Charles R Greathouse IV, Jul 26 2016

Formula

From R. J. Mathar, Jan 04 2011: (Start)

a(n) = 25*A003463(n).

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

G.f.: 25*x / ( (5*x-1)*(x-1) ). (End)

E.g.f.: (25/4)*(exp(5*x) - exp(x)). - G. C. Greubel, Jul 26 2016

Extensions

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