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%I M4990 N2147 #81 Jul 12 2023 12:27:54
%S 1,15,225,3375,50625,759375,11390625,170859375,2562890625,38443359375,
%T 576650390625,8649755859375,129746337890625,1946195068359375,
%U 29192926025390625,437893890380859375,6568408355712890625,98526125335693359375,1477891880035400390625,22168378200531005859375,332525673007965087890625
%N Powers of 15.
%C Same as Pisot sequences E(1, 15), L(1, 15), P(1, 15), T(1, 15). Essentially same as Pisot sequences E(15, 225), L(15, 225), P(15, 225), T(15, 225). See A008776 for definitions of Pisot sequences.
%C A000005(a(n)) = A000290(n+1). - _Reinhard Zumkeller_, Mar 04 2007
%C If X_1, X_2, ..., X_n is a partition of the set {1,2,...,2*n} into blocks of size 2 then, for n>=1, a(n) is equal to the number of functions f : {1,2,..., 2*n}->{1,2,3,4} such that for fixed y_1,y_2,...,y_n in {1,2,3,4} we have f(X_i)<>{y_i}, (i=1,2,...,n). - _Milan Janjic_, May 24 2007
%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 15-colored compositions of n such that no adjacent parts have the same color. - _Milan Janjic_, Nov 17 2011
%C Number of ways to assign truth values to n quaternary disjunctions connected by conjunctions such that the proposition is true. For example, a(2) = 225, since for the proposition (a v b v c v d) & (e v f v g v h) there are 225 assignments that make the proposition true. - _Ori Milstein_, Jan 26 2023
%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H T. D. Noe, <a href="/A001024/b001024.txt">Table of n, a(n) for n = 0..100</a>
%H P. J. Cameron, <a href="http://www.cs.uwaterloo.ca/journals/JIS/VOL3/groups.html">Sequences realized by oligomorphic permutation groups</a>, J. Integ. Seqs. Vol. 3 (2000), #00.1.5.
%H INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=279">Encyclopedia of Combinatorial Structures 279</a>
%H Milan Janjic, <a href="http://www.pmfbl.org/janjic/">Enumerative Formulas for Some Functions on Finite Sets</a>
%H Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>
%H Simon Plouffe, <a href="https://arxiv.org/abs/0911.4975">Approximations de séries génératrices et quelques conjectures</a>, Dissertation, Université du Québec à Montréal, 1992; arXiv:0911.4975 [math.NT], 2009.
%H Simon Plouffe, <a href="/A000051/a000051_2.pdf">1031 Generating Functions</a>, Appendix to Thesis, Montreal, 1992
%H Y. Puri and T. Ward, <a href="http://www.cs.uwaterloo.ca/journals/JIS/VOL4/WARD/short.html">Arithmetic and growth of periodic orbits</a>, J. Integer Seqs., Vol. 4 (2001), #01.2.1.
%H <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (15).
%F G.f.: 1/(1-15x), e.g.f.: exp(15x)
%F a(n) = 15^n; a(n) = 15*a(n-1) with a(0)=1. - _Vincenzo Librandi_, Nov 21 2010
%p A001024:=-1/(-1+15*z); # _Simon Plouffe_ in his 1992 dissertation
%t Table[15^n,{n,0,40}] (* _Vladimir Joseph Stephan Orlovsky_, Feb 15 2011 *)
%o (Magma) [ 15^n: n in [0..20] ]; // _Vincenzo Librandi_, Nov 21 2010
%o (Magma) [ n eq 1 select 1 else 15*Self(n-1): n in [1..21] ];
%o (PARI) a(n)=15^n \\ _Charles R Greathouse IV_, Sep 24 2015
%Y a(n) = A159991(n)/A000302(n). - _Reinhard Zumkeller_, May 02 2009
%Y Row 6 of A329332.
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_
%E More terms from _James A. Sellers_, Sep 19 2000
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