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%I #59 Aug 28 2023 14:37:28
%S 5,15,45,135,405,1215,3645,10935,32805,98415,295245,885735,2657205,
%T 7971615,23914845,71744535,215233605,645700815,1937102445,5811307335,
%U 17433922005,52301766015,156905298045,470715894135,1412147682405,4236443047215,12709329141645
%N a(n) = 5*3^n.
%H Vincenzo Librandi, <a href="/A005030/b005030.txt">Table of n, a(n) for n = 0..300</a>
%H Milan Janjic, <a href="http://www.pmfbl.org/janjic/">Enumerative Formulas for Some Functions on Finite Sets</a>
%H Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>
%H Jeffrey Ward, <a href="http://arxiv.org/abs/0806.1001">Does Ten Have a Friend?</a>, arXiv:0806.1001 [math.NT], 2008.
%H <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (3).
%F O.g.f.: 5/(1-3*x). - _R. J. Mathar_, Jan 31 2008
%F Limit_{n->oo} sigma(a(n))/a(n) = 9/5 = sigma(10)/10 (see Ward link). - _Michel Marcus_, Apr 30 2013
%F G.f.: 1/x + 2 - 2/x/G(0), where G(k)= 1 + 1/(1 - x*(5*k-3)/(x*(5*k+2) - 1/G(k+1))); (continued fraction). - _Sergei N. Gladkovskii_, Jun 04 2013
%F a(n) = 5*A000244(n). - _Michel Marcus_, Aug 25 2016
%F E.g.f.: 5*exp(3*x). - _Stefano Spezia_, Aug 28 2023
%t 5*3^Range[0, 60] (* _Vladimir Joseph Stephan Orlovsky_, Jun 09 2011 *)
%o (Magma) [5*3^n: n in [0..30]]; // _Vincenzo Librandi_, Jun 10 2011
%o (PARI) a(n)=5*3^n \\ _Charles R Greathouse IV_, Oct 07 2015
%Y Cf. A000244.
%K nonn,easy
%O 0,1
%A _N. J. A. Sloane_
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