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a(n) = n*3^n + 1.
5

%I #41 Sep 09 2024 18:46:02

%S 1,4,19,82,325,1216,4375,15310,52489,177148,590491,1948618,6377293,

%T 20726200,66961567,215233606,688747537,2195382772,6973568803,

%U 22082967874,69735688021,219667417264,690383311399,2165293113022,6778308875545,21182215236076,66088511536555,205891132094650

%N a(n) = n*3^n + 1.

%H Vincenzo Librandi, <a href="/A050914/b050914.txt">Table of n, a(n) for n = 0..1000</a>

%H 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 Paul Leyland, <a href="http://www.leyland.vispa.com/numth/factorization/cullen_woodall/cw.htm">Factors of Cullen and Woodall numbers</a>.

%H Paul Leyland, <a href="http://www.leyland.vispa.com/numth/factorization/cullen_woodall/gcw.htm">Generalized Cullen and Woodall numbers</a>.

%H 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 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (7,-15,9).

%F From _Colin Barker_, Oct 14 2012: (Start)

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

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

%F E.g.f.: exp(x)*(3*x*exp(2*x) + 1). - _Elmo R. Oliveira_, Sep 09 2024

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

%o (Magma) [ n*3^n+1: n in [0..20]]; // _Vincenzo Librandi_, Sep 16 2011

%o (PARI) a(n)=n*3^n+1 \\ _Charles R Greathouse IV_, Oct 07 2015

%Y Cf. A002064, A050915.

%Y Equals A036290(n) + 1.

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_, Dec 30 1999