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A001024
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Powers of 15.
(Formerly M4990 N2147)
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13
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1, 15, 225, 3375, 50625, 759375, 11390625, 170859375, 2562890625, 38443359375, 576650390625, 8649755859375, 129746337890625, 1946195068359375, 29192926025390625, 437893890380859375, 6568408355712890625, 98526125335693359375, 1477891880035400390625, 22168378200531005859375, 332525673007965087890625
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| A000005(a(n)) = A000290(n+1). - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Mar 04 2007
If X_1, X_2, ..., X_n is a partition of the set {1,2,...,2*n} into blocks of size 2 then, for n>=1, a(n) is equal to the number of functions f : {1,2,..., 2*n}->{1,2,3,4} such that for fixed y_1,y_2,...,y_n in {1,2,3,4} we have f(X_i)<>{y_i}, (i=1,2,...,n). - Milan R. Janjic (agnus(AT)blic.net), May 24 2007
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 15-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 279
Milan Janjic, Enumerative Formulas for Some Functions on Finite Sets
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/(1-15x), e.g.f.: exp(15x)
a(n) = 15^n; a(n) = 15*a(n-1) with a(0)=1. [From Vincenzo Librandi, Nov 21 2010]
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MAPLE
| A001024:=-1/(-1+15*z); [S. Plouffe in his 1992 dissertation.]
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MATHEMATICA
| Table[15^n, {n, 0, 40}] (*From Vladimir Joseph Stephan Orlovsky, Feb 15 2011*)
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PROG
| (Other) sage: [lucas_number1(n, 15, 0) for n in xrange(1, 18)]# [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 29 2009]
(MAGMA) [ 15^n: n in [0..20] ]; [From Vincenzo Librandi, Nov 21 2010]
(MAGMA) [ n eq 1 select 1 else 15*Self(n-1): n in [1..21] ];
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CROSSREFS
| a(n) = A159991(n)/A000302(n). [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), May 02 2009]
Sequence in context: A189338 A189774 A189156 * A012643 A067222 A154597
Adjacent sequences: A001021 A001022 A001023 * A001025 A001026 A001027
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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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