A050916 a(n) = n*5^n + 1.

1, 6, 51, 376, 2501, 15626, 93751, 546876, 3125001, 17578126, 97656251, 537109376, 2929687501, 15869140626, 85449218751, 457763671876, 2441406250001, 12969970703126, 68664550781251, 362396240234376, 1907348632812501, 10013580322265626, 52452087402343751

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (11,-35,25).

Formula

a(n) = 11*a(n-1) - 35*a(n-2) + 25*a(n-3); a(0)=1, a(1)=6, a(2)=51. - Harvey P. Dale, Sep 15 2011

G.f.: -(20*x^2-5*x+1)/((x-1)*(5*x-1)^2). - Colin Barker, Oct 14 2012

From Elmo R. Oliveira, May 03 2025: (Start)

E.g.f.: exp(x)*(1 + 5*x*exp(4*x)).

a(n) = A036291(n) + 1. (End)

Mathematica

Table[n 5^n+1, {n, 0, 20}] (* or *) LinearRecurrence[{11, -35, 25}, {1, 6, 51}, 20] (* Harvey P. Dale, Sep 15 2011 *)

Prog

(Magma) [ n*5^n+1: n in [0..20]]; // Vincenzo Librandi, Sep 16 2011

Crossrefs

Cf. A002064, A036291.

Sequence in context: A133395 A341424 A372731 * A376568 A011790 A292840

Adjacent sequences: A050913 A050914 A050915 * A050917 A050918 A050919

Keyword

nonn,easy

Author

N. J. A. Sloane, Dec 30 1999

Status

approved