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.
%I A009974 #43 Jul 10 2025 13:51:14 %S A009974 1,30,900,27000,810000,24300000,729000000,21870000000,656100000000, %T A009974 19683000000000,590490000000000,17714700000000000,531441000000000000, %U A009974 15943230000000000000,478296900000000000000,14348907000000000000000,430467210000000000000000,12914016300000000000000000 %N A009974 Powers of 30. %C A009974 Same as Pisot sequences E(1, 30), L(1, 30), P(1, 30), T(1, 30). Essentially same as Pisot sequences E(30, 900), L(30, 900), P(30, 900), T(30, 900). See A008776 for definitions of Pisot sequences. %C A009974 The compositions of n in which each natural number is colored by one of p different colors are called p-colored compositions of n. For n >= 1, a(n) equals the number of 30-colored compositions of n such that no adjacent parts have the same color. - _Milan Janjic_, Nov 17 2011 %H A009974 T. D. Noe, <a href="/A009974/b009974.txt">Table of n, a(n) for n = 0..100</a> %H A009974 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>. %H A009974 <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (30). %F A009974 G.f.: 1/(1-30*x). - _Philippe Deléham_, Nov 24 2008 %F A009974 a(n) = 30^n; a(n) = 30*a(n-1), n > 0; a(0)=1. - _Vincenzo Librandi_, Nov 21 2010 %F A009974 From _Elmo R. Oliveira_, Jul 10 2025: (Start) %F A009974 E.g.f.: exp(30*x). %F A009974 a(n) = A000244(n)*A011557(n) = A159991(n)/A000079(n). (End) %t A009974 NestList[30#&,1,20] (* _Harvey P. Dale_, Jul 21 2023 *) %o A009974 (Sage) [lucas_number1(n,30,0) for n in range(1, 17)] # _Zerinvary Lajos_, Apr 29 2009 %o A009974 (Magma)[30^n: n in [0..100]]; // _Vincenzo Librandi_, Nov 21 2010 %o A009974 (PARI) a(n)=30^n \\ _Charles R Greathouse IV_, Jun 19 2015 %o A009974 (PARI) powers(30,12) \\ _Charles R Greathouse IV_, Jun 19 2015 %Y A009974 Row 7 of A329332. %Y A009974 Cf. A000079, A000244, A008776, A011557, A159991. %K A009974 nonn,easy %O A009974 0,2 %A A009974 _N. J. A. Sloane_