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A001018
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Powers of 8.
(Formerly M4555 N1937)
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39
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1, 8, 64, 512, 4096, 32768, 262144, 2097152, 16777216, 134217728, 1073741824, 8589934592, 68719476736, 549755813888, 4398046511104, 35184372088832, 281474976710656, 2251799813685248, 18014398509481984, 144115188075855872, 1152921504606846976, 9223372036854775808, 73786976294838206464, 590295810358705651712
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Same as Pisot sequences E(1,8), L(1,8), P(1,8), T(1,8). See A008776 for definitions of Pisot sequences.
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} such that for fixed y_1,y_2,...,y_n in {1,2,3} we have f(X_i)<>{y_i}, (i=1,2,...,n). - Milan R. Janjic (agnus(AT)blic.net), May 24 2007
1/1 + 1/8 + 1/64 + 1/512 + 1/4096 + ... = 8/7 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Aug 29 2008]
a(n) = A157176(A008588(n)); a(n+1) = A157176(A016969(n)). [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Feb 24 2009]
This is the auto-convolution (convolution square) of A059304. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), May 25 2009]
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 8-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 273
Milan Janjic, Enumerative Formulas for Some Functions on Finite Sets
Tanya Khovanova, Recursive Sequences
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, Sierpinski Carpet
Index entries for sequences related to linear recurrences with constant coefficients
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FORMULA
| a(n) = 8^n; a(n) = 8a(n-1).
G.f.: 1/(1-8*x).
E.g.f.: exp(8*x).
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MAPLE
| seq(8^n, n=0..23); # Nathaniel Johnston, Jun 26 2011
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MATHEMATICA
| Table[8^n, {n, 0, 50}] (*From Vladimir Joseph Stephan Orlovsky, Feb 15 2011*)
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CROSSREFS
| A013730, A103333, A013731, A067417, A083233, A055274. [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Feb 24 2009]
Sequence in context: A190130 A125908 A206454 * A097682 A050738 A046238
Adjacent sequences: A001015 A001016 A001017 * A001019 A001020 A001021
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KEYWORD
| nonn,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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