A009980 - OEIS

%I #38 Jul 12 2023 12:42:28

%S 1,36,1296,46656,1679616,60466176,2176782336,78364164096,

%T 2821109907456,101559956668416,3656158440062976,131621703842267136,

%U 4738381338321616896,170581728179578208256,6140942214464815497216

%N Powers of 36.

%C 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 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 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 T. D. Noe, <a href="/A009980/b009980.txt">Table of n, a(n) for n = 0..100</a>

%H Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>

%H <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (36).

%F G.f.: 1/(1-36*x). - _Philippe Deléham_, Nov 24 2008

%F a(n) = 36^n; a(n) = 36 * a(n-1) for n > 0, a(0) = 1. - _Vincenzo Librandi_, Nov 21 2010

%t 36^Range[0, 20]  (* _Harvey P. Dale_, Mar 04 2011 *)

%o (Magma)[36^n: n in [0..20]] // _Vincenzo Librandi_, Nov 21 2010

%o (PARI) a(n)=36^n \\ _Charles R Greathouse IV_, Nov 18 2011

%Y Cf. A000400.

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_.