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%I #31 Jul 12 2023 12:50:50
%S 1,49,2401,117649,5764801,282475249,13841287201,678223072849,
%T 33232930569601,1628413597910449,79792266297612001,
%U 3909821048582988049,191581231380566414401,9387480337647754305649,459986536544739960976801
%N Powers of 49.
%C Same as Pisot sequences E(1, 49), L(1, 49), P(1, 49), T(1, 49). Essentially same as Pisot sequences E(49, 2401), L(49, 2401), P(49, 2401), T(49, 2401). 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 49-colored compositions of n such that no adjacent parts have the same color. - _Milan Janjic_, Nov 17 2011
%H T. D. Noe, <a href="/A087752/b087752.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 (49).
%F G.f.: 1/(1-49*x). - _Philippe Deléham_, Nov 24 2008
%F From _Vincenzo Librandi_, Nov 21 2010: (Start)
%F a(n) = 49^n;
%F a(n) = 49*a(n-1), a(0)=1. (End)
%t 49^Range[0,20] (* or *) Join[{1},NestList[49#&,49,20]] (* _Harvey P. Dale_, May 10 2019 *)
%o (Magma) [49^n: n in [0..20]]; // _Vincenzo Librandi_, Nov 21 2010
%o (Maxima) makelist(49^n,n,0,20); /* _Martin Ettl_, Nov 12 2012 */
%o (PARI) a(n)=49^n \\ _M. F. Hasler_, Apr 19 2015
%Y Cf. A001018 (powers of 8), ..., A001029 (powers of 19), A009964 (powers of 20), ..., A009992 (powers of 48).
%K easy,nonn
%O 0,2
%A Douglas Winston (douglas.winston(AT)srupc.com), Oct 02 2003
%E Edited by _M. F. Hasler_, Apr 19 2015
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