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A001027
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Powers of 18.
(Formerly M5062 N2192)
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9
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| 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
| 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
| 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
S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
S. Plouffe, 1031 Generating Functions and Conjectures, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
Y. Puri and T. Ward, Arithmetic and growth of periodic orbits, J. Integer Seqs., Vol. 4 (2001), #01.2.1.
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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. [From Vincenzo Librandi, Nov 21 2010]
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MAPLE
| A001027:=-1/(-1+18*z); [S. Plouffe in his 1992 dissertation.]
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MATHEMATICA
| Table[18^n, {n, 0, 40}] (*From Vladimir Joseph Stephan Orlovsky, Feb 15 2011*)
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PROG
| sage: from sage.combinat.sloane_functions import recur_gen2b sage: it =recur_gen2b(1, n/3, n/3, 0, lambda n: 0) sage: [it.next() for i in range(18)] - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 16 2008
(Other) sage: [lucas_number1(n, 18, 0) for n in xrange(1, 17)]# [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 29 2009]
(MAGMA)[ 18^n: n in [0..20] ]; [From Vincenzo Librandi, Nov 21 2010]
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CROSSREFS
| Sequence in context: A207109 A207240 A171292 * A041145 A041614 A166787
Adjacent sequences: A001024 A001025 A001026 * A001028 A001029 A001030
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| More terms from James A. Sellers (sellersj(AT)math.psu.edu), Sep 19 2000
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