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A009984 Powers of 40.

%I A009984 #37 Jul 10 2025 13:51:05
%S A009984 1,40,1600,64000,2560000,102400000,4096000000,163840000000,
%T A009984 6553600000000,262144000000000,10485760000000000,419430400000000000,
%U A009984 16777216000000000000,671088640000000000000,26843545600000000000000,1073741824000000000000000,42949672960000000000000000
%N A009984 Powers of 40.
%C A009984 Same as Pisot sequences E(1, 40), L(1, 40), P(1, 40), T(1, 40). Essentially same as Pisot sequences E(40, 1600), L(40, 1600), P(40, 1600), T(40, 1600). See A008776 for definitions of Pisot sequences.
%C A009984 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 40-colored compositions of n such that no adjacent parts have the same color. - _Milan Janjic_, Nov 17 2011
%H A009984 T. D. Noe, <a href="/A009984/b009984.txt">Table of n, a(n) for n = 0..100</a>
%H A009984 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>.
%H A009984 <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (40).
%F A009984 G.f.: 1/(1 - 40*x). - _Philippe Deléham_, Nov 24 2008
%F A009984 a(n) = 40^n; a(n) = 40*a(n-1), a(0) = 1. - _Vincenzo Librandi_, Nov 21 2010
%F A009984 From _Elmo R. Oliveira_, Jul 10 2025: (Start)
%F A009984 E.g.f.: exp(40*x).
%F A009984 a(n) = A000079(n)*A009964(n) = A259076(n)/A000079(n). (End)
%t A009984 40^Range[0, 19] (* _Alonso del Arte_, Sep 04 2016 *)
%o A009984 (Magma) [40^n: n in [0..20]]; // _Vincenzo Librandi_, Nov 21 2010
%o A009984 (PARI) a(n)=40^n \\ _Charles R Greathouse IV_, Jun 19 2015
%o A009984 (PARI) powers(40,10) \\ _Charles R Greathouse IV_, Jun 19 2015
%Y A009984 Cf. A000079, A000302, A008776, A009964, A011557, A259076.
%K A009984 nonn,easy
%O A009984 0,2
%A A009984 _N. J. A. Sloane_, Dec 11 1996