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A009972 Powers of 28.

%I A009972 #44 Jul 10 2025 08:13:17
%S A009972 1,28,784,21952,614656,17210368,481890304,13492928512,377801998336,
%T A009972 10578455953408,296196766695424,8293509467471872,232218265089212416,
%U A009972 6502111422497947648,182059119829942534144,5097655355238390956032,142734349946674946768896,3996561798506898509529088
%N A009972 Powers of 28.
%C A009972 Same as Pisot sequences E(1, 28), L(1, 28), P(1, 28), T(1, 28). Essentially same as Pisot sequences E(28, 784), L(28, 784), P(28, 784), T(28, 784). See A008776 for definitions of Pisot sequences.
%C A009972 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 28-colored compositions of n such that no adjacent parts have the same color. - _Milan Janjic_, Nov 17 2011
%H A009972 T. D. Noe, <a href="/A009972/b009972.txt">Table of n, a(n) for n = 0..100</a>
%H A009972 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>.
%H A009972 <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (28).
%F A009972 G.f.: 1/(1-28*x). - _Philippe Deléham_, Nov 24 2008
%F A009972 a(n) = 28^n; a(n) = 28*a(n-1), n > 0, a(0) = 1. - _Vincenzo Librandi_, Nov 21 2010
%F A009972 From _Elmo R. Oliveira_, Jul 10 2025: (Start)
%F A009972 E.g.f.: exp(28*x).
%F A009972 a(n) = A000079(n)*A001023(n) = A000302(n)*A000420(n). (End)
%t A009972 28^Range[0, 13] (* _Alonso del Arte_, Feb 28 2015 *)
%t A009972 NestList[28#&,1,20] (* _Harvey P. Dale_, Jan 19 2019 *)
%o A009972 (Sage) [lucas_number1(n,28,0) for n in range(1, 17)] # _Zerinvary Lajos_, Apr 29 2009
%o A009972 (Magma) [28^n: n in [0..100]]; // _Vincenzo Librandi_, Nov 21 2010
%o A009972 (PARI) a(n)=28^n \\ _Charles R Greathouse IV_, Sep 28 2015
%Y A009972 Cf. A000079, A000302, A000420, A001023, A008776.
%K A009972 nonn,easy
%O A009972 0,2
%A A009972 _N. J. A. Sloane_