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
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).
Programs
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Magma
[ n*3^n+1: n in [0..20]]; // Vincenzo Librandi, Sep 16 2011
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Mathematica
Table[n*3^n+1,{n,0,30}] (* or *) LinearRecurrence[{7,-15,9},{1,4,19},30] (* Harvey P. Dale, Nov 07 2012 *) -
PARI
a(n)=n*3^n+1 \\ Charles R Greathouse IV, Oct 07 2015
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