cp's OEIS Frontend

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

%I A050914 #41 Sep 09 2024 18:46:02
%S A050914 1,4,19,82,325,1216,4375,15310,52489,177148,590491,1948618,6377293,
%T A050914 20726200,66961567,215233606,688747537,2195382772,6973568803,
%U A050914 22082967874,69735688021,219667417264,690383311399,2165293113022,6778308875545,21182215236076,66088511536555,205891132094650
%N A050914 a(n) = n*3^n + 1.
%H A050914 Vincenzo Librandi, <a href="/A050914/b050914.txt">Table of n, a(n) for n = 0..1000</a>
%H A050914 Jon Grantham and Hester Graves, <a href="https://arxiv.org/abs/2009.04052">The abc Conjecture Implies That Only Finitely Many Cullen Numbers Are Repunits</a>, arXiv:2009.04052 [math.NT], 2020.
%H A050914 Paul Leyland, <a href="http://www.leyland.vispa.com/numth/factorization/cullen_woodall/cw.htm">Factors of Cullen and Woodall numbers</a>.
%H A050914 Paul Leyland, <a href="http://www.leyland.vispa.com/numth/factorization/cullen_woodall/gcw.htm">Generalized Cullen and Woodall numbers</a>.
%H A050914 Amelia Carolina Sparavigna, <a href="https://doi.org/10.18483/ijSci.2188">Some Groupoids and their Representations by Means of Integer Sequences</a>, International Journal of Sciences (2019) Vol. 8, No. 10.
%H A050914 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (7,-15,9).
%F A050914 From _Colin Barker_, Oct 14 2012: (Start)
%F A050914 a(n) = 7*a(n-1) - 15*a(n-2) + 9*a(n-3).
%F A050914 G.f.: -(6*x^2 - 3*x + 1)/((x-1)*(3*x-1)^2). (End)
%F A050914 E.g.f.: exp(x)*(3*x*exp(2*x) + 1). - _Elmo R. Oliveira_, Sep 09 2024
%t A050914 Table[n*3^n+1,{n,0,30}] (* or *) LinearRecurrence[{7,-15,9},{1,4,19},30] (* _Harvey P. Dale_, Nov 07 2012 *)
%o A050914 (Magma) [ n*3^n+1: n in [0..20]]; // _Vincenzo Librandi_, Sep 16 2011
%o A050914 (PARI) a(n)=n*3^n+1 \\ _Charles R Greathouse IV_, Oct 07 2015
%Y A050914 Cf. A002064, A050915.
%Y A050914 Equals A036290(n) + 1.
%K A050914 nonn,easy
%O A050914 0,2
%A A050914 _N. J. A. Sloane_, Dec 30 1999