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A001027 Powers of 18.
(Formerly M5062 N2192)
20
1, 18, 324, 5832, 104976, 1889568, 34012224, 612220032, 11019960576, 198359290368, 3570467226624, 64268410079232, 1156831381426176, 20822964865671168, 374813367582081024, 6746640616477458432, 121439531096594251776, 2185911559738696531968, 39346408075296537575424, 708235345355337676357632, 12748236216396078174437376 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
Same as Pisot sequences E(1, 18), L(1, 18), P(1, 18), T(1, 18). Essentially same as Pisot sequences E(18, 324), L(18, 324), P(18, 324), T(18, 324). See A008776 for definitions of Pisot sequences.
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
REFERENCES
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).
LINKS
P. J. Cameron, Sequences realized by oligomorphic permutation groups, J. Integ. Seqs. Vol. 3 (2000), #00.1.5.
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.
FORMULA
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
MAPLE
A001027:=-1/(-1+18*z); # Simon Plouffe in his 1992 dissertation
MATHEMATICA
Table[18^n, {n, 0, 40}] (* Vladimir Joseph Stephan Orlovsky, Feb 15 2011 *)
PROG
(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
CROSSREFS
Sequence in context: A207498 A285878 A171292 * A285875 A223311 A041145
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
More terms from James A. Sellers, Sep 19 2000
STATUS
approved

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Last modified June 19 07:40 EDT 2024. Contains 373492 sequences. (Running on oeis4.)