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%I #35 Apr 14 2023 17:07:16
%S 3,27,243,2187,19683,177147,1594323,14348907,129140163,1162261467,
%T 10460353203,94143178827,847288609443,7625597484987,68630377364883,
%U 617673396283947,5559060566555523,50031545098999707
%N a(n) = 3^(2n+1).
%C 1/3 + 1/27 + 1/243 + ... = 3/8. - _Gary W. Adamson_, Aug 29 2008
%C Number n such that if a=n, b=8n, c=15n, d=36n*sqrt(3n), then a^3 + b^3 + c^3 = d^2; e.g.: a=3, b=24, c=45, d=324, 3^3 + 24^3 + 45^3 = 324^2. - _Vincenzo Librandi_, Nov 20 2010
%H Delbert L. Johnson, <a href="/A013708/b013708.txt">Table of n, a(n) for n = 0..1047</a>
%H Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>
%H R. J. Mathar, <a href="/A102518/a102518.pdf">Counting Walks on Finite Graphs</a>, Nov 2020, Section 4.
%H <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (9).
%F From _Philippe Deléham_, Nov 23 2008: (Start)
%F a(n) = 9*a(n-1), n > 0; a(0)=3.
%F G.f.: 3/(1-9x). (End)
%F a(n) = A000244(2n+1). - _R. J. Mathar_, Jul 10 2015
%t NestList[9#&,3,20] (* _Harvey P. Dale_, Apr 21 2014 *)
%o (PARI) a(n)=3^(2*n+1) \\ _Charles R Greathouse IV_, Aug 05 2015
%o (Python)
%o print([3**(2*n+1) for n in range(18)]) # _Michael S. Branicky_, Mar 27 2021
%Y Cf. A000244.
%K nonn,easy
%O 0,1
%A _N. J. A. Sloane_
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