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A000400
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Powers of 6.
(Formerly M4224 N1765)
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58
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1, 6, 36, 216, 1296, 7776, 46656, 279936, 1679616, 10077696, 60466176, 362797056, 2176782336, 13060694016, 78364164096, 470184984576, 2821109907456, 16926659444736, 101559956668416, 609359740010496, 3656158440062976, 21936950640377856, 131621703842267136
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Same as Pisot sequences E(1,6), L(1,6), P(1,6), T(1,6). See A008776 for definitions of Pisot sequences.
Central terms of the triangle in A036561. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), May 14 2006
A000005(a(n)) = A000290(n+1). - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Mar 04 2007
a(n) = A169604(n)/3; a(n+1) = 2*A169604(n). [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), May 02 2010]
Number of pentagons contained within pentaflakes. [From William A. Tedeschi (fynmun(AT)att.net), Sep 12 2010]
Sum of coefficients of expansion of (1+x+x^2+x^3+x^4+x^5)^n.
a(n) is number of compositions of natural numbers into n parts <6.
a(2)=36 there are 36 compositions of natural numbers into 2 parts <6.
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 5-colored compositions of n such that no adjacent parts have the same color.
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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
C. Banderier and D. Merlini, Lattice paths with an infinite set of jumps, FPSAC02, Melbourne, 2002.
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 271
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.
Eric Weisstein's World of Mathematics, Pentaflake [From William A. Tedeschi (fynmun(AT)att.net), Sep 12 2010]
Index entries for sequences related to linear recurrences with constant coefficients
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FORMULA
| a(n) = 6^n.
a(n) = 6*a(n-1).
G.f.: 1/(1-6*x).
E.g.f.: exp(6*x).
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MAPLE
| A000400:=-1/(-1+6*z); [S. Plouffe in his 1992 dissertation.]
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MATHEMATICA
| Table[6^n, {n, 40}] [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Feb 19 2010]
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PROG
| (PARI) a(n)=6^n \\ Charles R Greathouse IV, Jun 16 2011
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CROSSREFS
| a(n) = A159991(n)/A011577(n). [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), May 02 2009]
Sequence in context: A126634 A007275 A206452 * A097681 A050736 A196869
Adjacent sequences: A000397 A000398 A000399 * A000401 A000402 A000403
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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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