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A001027
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Powers of 18.
(Formerly M5062 N2192)
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22
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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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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
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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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FORMULA
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G.f.: 1/(1-18x), e.g.f.: exp(18x).
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MAPLE
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MATHEMATICA
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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
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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