A050914 a(n) = n*3^n + 1.

1, 4, 19, 82, 325, 1216, 4375, 15310, 52489, 177148, 590491, 1948618, 6377293, 20726200, 66961567, 215233606, 688747537, 2195382772, 6973568803, 22082967874, 69735688021, 219667417264, 690383311399, 2165293113022, 6778308875545, 21182215236076, 66088511536555, 205891132094650

Offset

0,2

Links

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

Jon Grantham and Hester Graves, The abc Conjecture Implies That Only Finitely Many Cullen Numbers Are Repunits, arXiv:2009.04052 [math.NT], 2020.

Paul Leyland, Factors of Cullen and Woodall numbers.

Paul Leyland, Generalized Cullen and Woodall numbers.

Amelia Carolina Sparavigna, Some Groupoids and their Representations by Means of Integer Sequences, International Journal of Sciences (2019) Vol. 8, No. 10.

Index entries for linear recurrences with constant coefficients, signature (7,-15,9).

Formula

From Colin Barker, Oct 14 2012: (Start)

a(n) = 7*a(n-1) - 15*a(n-2) + 9*a(n-3).

G.f.: -(6*x^2 - 3*x + 1)/((x-1)*(3*x-1)^2). (End)

E.g.f.: exp(x)*(3*x*exp(2*x) + 1). - Elmo R. Oliveira, Sep 09 2024

Mathematica

Table[n*3^n+1, {n, 0, 30}] (* or *) LinearRecurrence[{7, -15, 9}, {1, 4, 19}, 30] (* Harvey P. Dale, Nov 07 2012 *)

Prog

(Magma) [ n*3^n+1: n in [0..20]]; // Vincenzo Librandi, Sep 16 2011
(PARI) a(n)=n*3^n+1 \\ Charles R Greathouse IV, Oct 07 2015

Crossrefs

Cf. A002064, A050915.

Equals A036290(n) + 1.

Sequence in context: A181300 A027240 A326649 * A017961 A180146 A017962

Adjacent sequences: A050911 A050912 A050913 * A050915 A050916 A050917

Keyword

nonn,easy

Author

N. J. A. Sloane, Dec 30 1999

Status

approved