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A009980 Powers of 36.

%I A009980 #45 Jul 10 2025 13:51:09
%S A009980 1,36,1296,46656,1679616,60466176,2176782336,78364164096,
%T A009980 2821109907456,101559956668416,3656158440062976,131621703842267136,
%U A009980 4738381338321616896,170581728179578208256,6140942214464815497216,221073919720733357899776,7958661109946400884391936
%N A009980 Powers of 36.
%C A009980 Same as Pisot sequences E(1, 36), L(1, 36), P(1, 36), T(1, 36). Essentially same as Pisot sequences E(36, 1296), L(36, 1296), P(36, 1296), T(36, 1296). See A008776 for definitions of Pisot sequences.
%C A009980 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 36-colored compositions of n such that no adjacent parts have the same color. - _Milan Janjic_, Nov 17 2011
%C A009980 See _David Applegate_'s comment in A000244 from Feb 20 2017 for a proof of Janjic's assertion. - _Alonso del Arte_, Sep 03 2017
%H A009980 T. D. Noe, <a href="/A009980/b009980.txt">Table of n, a(n) for n = 0..100</a>
%H A009980 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>.
%H A009980 <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (36).
%F A009980 G.f.: 1/(1-36*x). - _Philippe Deléham_, Nov 24 2008
%F A009980 a(n) = 36^n; a(n) = 36*a(n-1) for n > 0, a(0) = 1. - _Vincenzo Librandi_, Nov 21 2010
%F A009980 From _Elmo R. Oliveira_, Jul 10 2025: (Start)
%F A009980 E.g.f.: exp(36*x).
%F A009980 a(n) = A000079(n)*A001027(n) = A000400(A005843(n)). (End)
%t A009980 36^Range[0, 20]  (* _Harvey P. Dale_, Mar 04 2011 *)
%o A009980 (Magma)[36^n: n in [0..20]]; // _Vincenzo Librandi_, Nov 21 2010
%o A009980 (PARI) a(n)=36^n \\ _Charles R Greathouse IV_, Nov 18 2011
%Y A009980 Cf. A000079, A000244, A000400, A001027, A005843, A008776.
%K A009980 nonn,easy
%O A009980 0,2
%A A009980 _N. J. A. Sloane_