%I A052944
%S A052944 0,2,5,10,19,36,69,134,263,520,1033,2058,4107,8204,16397,32782,65551,
%T A052944 131088,262161,524306,1048595,2097172,4194325,8388630,16777239,
%U A052944 33554456,67108889,134217754,268435483,536870940,1073741853,2147483678
%N A052944 a(n) = 2^n + n - 1
%C A052944 Shortest length of bitstring containing all bitstrings of given length. 
               - Rainer Rosenthal (r.rosenthal(AT)web.de), Apr 30 2003
%C A052944 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
%D A052944 Discussed in newsgroup de.rec.denksport in Apr 2003
%D A052944 N. G. de Bruijn: A combinatorial problem. Indagationes Math. 8 (1946), 
               pp. 461-467.
%H A052944 INRIA Algorithms Project, <a href="http://algo.inria.fr/bin/encyclopedia?Search=ECSnb&argsearch=1001">
               Encyclopedia of Combinatorial Structures 1001</a>
%H A052944 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               CyclotomicPolynomial.html">Cyclotomic Polynomial</a>
%H A052944 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               CoinTossing.html">Coin Tossing</a>
%F A052944 G.f.: (2-3*x)/((1-2*x)*(1-x)^2).
%F A052944 a(n+1)=2*a(n)-n+2 with a(0)=0. - Pieter Moree, Mar 06 2004
%F A052944 For n>=1: partial sums of A000051. - Emeric Deutsch (deutsch(AT)duke.poly.edu), 
               Mar 04 2004
%F A052944 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
%F A052944 a(n) =A000225+n [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 
               May 29 2009]
%e A052944 a(3)=10 because "0001110100" has length 10 and contains all possible 
               patterns of 3 bit.
%p A052944 spec := [S,{S=Prod(Union(Sequence(Union(Z,Z)),Sequence(Z)),Sequence(Z))},
               unlabeled ]: seq(combstruct[count ](spec,size=n), n=0..20);
%p A052944 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]
%t A052944 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]
%o A052944 (Other) sage: [gaussian_binomial(n,1,2)+n for n in xrange(0,32)] # [From 
               Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 29 2009]
%Y A052944 Cf. A000215 (Fermat number).
%Y A052944 Cf. A000051.
%Y A052944 A160692. [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), 
               May 24 2009]
%Y A052944 Sequence in context: A104161 A065613 A061705 this_sequence A132736 A068035 
               A016029
%Y A052944 Adjacent sequences: A052941 A052942 A052943 this_sequence A052945 A052946 
               A052947
%K A052944 easy,nonn
%O A052944 0,2
%A A052944 encyclopedia(AT)pommard.inria.fr, Jan 25 2000
%E A052944 More terms from James A. Sellers (sellersj(AT)math.psu.edu), Jun 05 2000