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Search: id:A052944
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| 0, 2, 5, 10, 19, 36, 69, 134, 263, 520, 1033, 2058, 4107, 8204, 16397, 32782, 65551, 131088, 262161, 524306, 1048595, 2097172, 4194325, 8388630, 16777239, 33554456, 67108889, 134217754, 268435483, 536870940, 1073741853, 2147483678
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Shortest length of bitstring containing all bitstrings of given length. - Rainer Rosenthal (r.rosenthal(AT)web.de), Apr 30 2003
Also the indices of Fermat numbers that can be represented as cyclotomic numbers. Specifically, F(a(n)) = cyclotomic(2^2^n,2^2^n). - T. D. Noe (noe(AT)sspectra.com), Oct 17 2003
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REFERENCES
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Discussed in newsgroup de.rec.denksport in Apr 2003
N. G. de Bruijn: A combinatorial problem. Indagationes Math. 8 (1946), pp. 461-467.
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LINKS
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INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 1001
Eric Weisstein's World of Mathematics, Cyclotomic Polynomial
Eric Weisstein's World of Mathematics, Coin Tossing
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FORMULA
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G.f.: (2-3*x)/((1-2*x)*(1-x)^2).
a(n+1)=2*a(n)-n+2 with a(0)=0. - Pieter Moree, Mar 06 2004
For n>=1: partial sums of A000051. - Emeric Deutsch (deutsch(AT)duke.poly.edu), Mar 04 2004
a(0)=0, a(1)=2, a(2)=5, a(n+3)=4a(n+2)-5a(n+1)+2a(n). - Hermann Kremer (Hermann.Kremer(AT)online.de), Mar 16 2004
a(n) =A000225+n [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 29 2009]
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EXAMPLE
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a(3)=10 because "0001110100" has length 10 and contains all possible patterns of 3 bit.
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MAPLE
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spec := [S, {S=Prod(Union(Sequence(Union(Z, Z)), Sequence(Z)), Sequence(Z))}, unlabeled ]: seq(combstruct[count ](spec, size=n), n=0..20);
restart:a:=n->sum(1+2^j, j=0..n): seq(a(n), n=-1..30); # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 18 2009]
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MATHEMATICA
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lst={}; Do[AppendTo[lst, 2^n+n-1], {n, 0, 4!}]; lst...and/or... s=-5; lst={0, 2, Abs[s]}; Do[s+=s+n++; AppendTo[lst, Abs[s]], {n, 0, 4!-2}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Oct 25 2008]
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PROGRAM
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(Other) sage: [gaussian_binomial(n, 1, 2)+n for n in xrange(0, 32)] # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 29 2009]
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CROSSREFS
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Cf. A000215 (Fermat number).
Cf. A000051.
A160692. [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), May 24 2009]
Sequence in context: A104161 A065613 A061705 this_sequence A132736 A068035 A016029
Adjacent sequences: A052941 A052942 A052943 this_sequence A052945 A052946 A052947
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KEYWORD
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easy,nonn
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AUTHOR
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encyclopedia(AT)pommard.inria.fr, Jan 25 2000
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EXTENSIONS
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More terms from James A. Sellers (sellersj(AT)math.psu.edu), Jun 05 2000
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