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A001027
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Powers of 18.
(Formerly M5062 N2192)
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20
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1, 18, 324, 5832, 104976, 1889568, 34012224, 612220032, 11019960576, 198359290368, 3570467226624, 64268410079232, 1156831381426176, 20822964865671168, 374813367582081024, 6746640616477458432, 121439531096594251776, 2185911559738696531968, 39346408075296537575424, 708235345355337676357632, 12748236216396078174437376
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OFFSET
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0,2
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COMMENTS
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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 18-colored compositions of n such that no adjacent parts have the same color. - Milan Janjic, Nov 17 2011
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REFERENCES
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N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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T. D. Noe, Table of n, a(n) for n = 0..100
P. J. Cameron, Sequences realized by oligomorphic permutation groups, J. Integ. Seqs. Vol. 3 (2000), #00.1.5.
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 282
Tanya Khovanova, Recursive Sequences
Simon Plouffe, Approximations de séries génératrices et quelques conjectures, Dissertation, Université du Québec à Montréal, 1992; arXiv:0911.4975 [math.NT], 2009.
Simon Plouffe, 1031 Generating Functions, Appendix to Thesis, Montreal, 1992
Y. Puri and T. Ward, Arithmetic and growth of periodic orbits, J. Integer Seqs., Vol. 4 (2001), #01.2.1.
Index entries for linear recurrences with constant coefficients, signature (18).
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FORMULA
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G.f.: 1/(1-18x), e.g.f.: exp(18x).
a(n) = 18^n; a(n) = 18*a(n-1) with a(0)=1. - Vincenzo Librandi, Nov 21 2010
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MAPLE
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A001027:=-1/(-1+18*z); # Simon Plouffe in his 1992 dissertation
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MATHEMATICA
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Table[18^n, {n, 0, 40}] (* Vladimir Joseph Stephan Orlovsky, Feb 15 2011 *)
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PROG
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(Sage) [18**n for n in range(20)] # F. Chapoton, Feb 23 2020
(Sage) [lucas_number1(n, 18, 0) for n in range(1, 17)] # Zerinvary Lajos, Apr 29 2009
(MAGMA) [ 18^n: n in [0..20] ]; // Vincenzo Librandi, Nov 21 2010
(PARI) a(n)=18^n \\ Charles R Greathouse IV, Sep 28 2015
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CROSSREFS
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Sequence in context: A207498 A285878 A171292 * A285875 A223311 A041145
Adjacent sequences: A001024 A001025 A001026 * A001028 A001029 A001030
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane
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EXTENSIONS
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More terms from James A. Sellers, Sep 19 2000
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STATUS
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approved
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