cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A005051 a(n) = 8*3^n.

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%I A005051 #38 Aug 16 2024 19:18:42
%S A005051 8,24,72,216,648,1944,5832,17496,52488,157464,472392,1417176,4251528,
%T A005051 12754584,38263752,114791256,344373768,1033121304,3099363912,
%U A005051 9298091736,27894275208,83682825624,251048476872,753145430616,2259436291848,6778308875544,20334926626632
%N A005051 a(n) = 8*3^n.
%C A005051 For n>=3, a(n-3) is equal to the number of functions f:{1,2,...,n}->{1,2,3} such that for fixed, different x_1, x_2, x_3 in {1,2,...,n} and fixed y_1, y_2, y_3 in {1,2,3} we have f(x_i)<>y_i, (i=1,2,3). - _Milan Janjic_, May 13 2007
%H A005051 Vincenzo Librandi, <a href="/A005051/b005051.txt">Table of n, a(n) for n = 0..300</a>
%H A005051 Milan Janjic, <a href="https://pmf.unibl.org/wp-content/uploads/2017/10/enumfun.pdf">Enumerative Formulas for Some Functions on Finite Sets</a>
%H A005051 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>
%H A005051 <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (3).
%F A005051 a(n) = 3*a(n-1). G.f.: 8/(1-3*x). - _Colin Barker_, Jul 02 2012
%F A005051 From _Elmo R. Oliveira_, Aug 16 2024: (Start)
%F A005051 E.g.f.: 8*exp(3*x).
%F A005051 a(n) = 8*A000244(n) = 4*A008776(n). (End)
%t A005051 8*3^Range[0, 60] (* _Vladimir Joseph Stephan Orlovsky_, Jun 09 2011 *)
%o A005051 (Magma) [8*3^n: n in [0..30]]; // _Vincenzo Librandi_, Jun 10 2011
%o A005051 (PARI) a(n)=8*3^n \\ _Charles R Greathouse IV_, Sep 28 2015
%Y A005051 Cf. A000244, A008776.
%K A005051 nonn,easy
%O A005051 0,1
%A A005051 _N. J. A. Sloane_