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A001019
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Powers of 9.
(Formerly M4653 N1992)
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36
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1, 9, 81, 729, 6561, 59049, 531441, 4782969, 43046721, 387420489, 3486784401, 31381059609, 282429536481, 2541865828329, 22876792454961, 205891132094649, 1853020188851841, 16677181699666569, 150094635296999121, 1350851717672992089
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Same as Pisot sequences E(1,9), L(1,9), P(1,9), T(1,9). See A008776 for definitions of Pisot sequences.
Except for 1, the largest n-th power with n digits. - Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Feb 09 2002
The 2002 comment by Amarnath Murthy should say more precisely "n-th power with *at most* n digits": a(22) has only 21 digits etc., a(44) has only 42 digits etc. [From Hagen von Eitzen (math(AT)von-eitzen.de), May 17 2009]
A000005(a(n)) = A005408(n+1). - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Mar 04 2007
1/1 + 1/9 + 1/81 + ... = 9/8 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Aug 29 2008]
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 9-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 274
Tanya Khovanova, Recursive Sequences
Y. Puri and T. Ward, Arithmetic and growth of periodic orbits, J. Integer Seqs., Vol. 4 (2001), #01.2.1.
Index entries for sequences related to linear recurrences with constant coefficients
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FORMULA
| a(n) = 9^n; a(n) = 9*a(n-1).
G.f.: 1/(1-9*x)
E.g.f.: exp(9*x)
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MATHEMATICA
| Table[9^n, {n, 0, 40}] (*From Vladimir Joseph Stephan Orlovsky, Feb 15 2011*)
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CROSSREFS
| Cf. A067470.
Sequence in context: A120997 A125630 A100062 * A074118 A050739 A158779
Adjacent sequences: A001016 A001017 A001018 * A001020 A001021 A001022
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KEYWORD
| easy,nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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