Search: id:A002416
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%I A002416
%S A002416 1,2,16,512,65536,33554432,68719476736,562949953421312,18446744073709551616,
%T A002416 2417851639229258349412352,1267650600228229401496703205376,2658455991569831745807614120560689152,
%U A002416 22300745198530623141535718272648361505980416,748288838313422294120286634350736906063837462003712
%N A002416 2^(n^2).
%C A002416 For n >= 1 a(n) is the number of n X n (0,1) matrices.
%C A002416 1/2^(n^2) is the Hankel transform of C(n,n/2)(1+(-1)^n)/(2*2^n), or C(2n,
               n)/4^n with interpolated zeros. - Paul Barry (pbarry(AT)wit.ie), 
               Sep 27 2007
%C A002416 Hankel transform of A064062 . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), 
               Nov 19 2007
%C A002416 a(n) is also the order of the semigroup (monoid) of all binary relations 
               on an n-set. [From A. Umar (aumarh(AT)squ.edu.om), Sep 14 2008]
%D A002416 F. Harary and R. W. Robinson, Labeled bipartite blocks, Canad. J. Math., 
               31 (1979), 60-68.
%D A002416 Kent E. Morrison, Integer Sequences and Matrices Over Finite Fields, 
               Journal of Integer Sequences, Vol. 9 (2006), Article 06.2.1.
%D A002416 Howie, J. M. Fundamentals of semigroup theory. Oxford: Clarendon Press, 
               (1995). [From A. Umar (aumarh(AT)squ.edu.om), Sep 14 2008]
%H A002416 P. J. Cameron, <a href="http://www.cs.uwaterloo.ca/journals/JIS/index.html">
               Sequences realized by oligomorphic permutation groups</a>, J. Integ. 
               Seqs. Vol. 3 (2000), #00.1.5.
%H A002416 T. Eisenkoelbl, <a href="http://www.arXiv.org/abs/math.CO/0106038">2-Enumerations 
               of halved alternating sign matrices</a>.
%H A002416 T. Eisenk\"olbl, <a href="http://www.mat.univie.ac.at/~slc/opapers/s46eisenko.html">
               2-Enumerations of halved alternating sign matrices</a>
%H A002416 Daniele A. Gewurz and Francesca Merola, <a href="http://www.cs.uwaterloo.ca/
               journals/JIS/index.html">Sequences realized as Parker vectors ...</
               a>, J. Integer Seqs., Vol. 6, 2003.
%H A002416 G. Pfeiffer, <a href="http://www.cs.uwaterloo.ca/journals/JIS/">Counting 
               Transitive Relations</a>, Journal of Integer Sequences, Vol. 7 (2004), 
               Article 04.3.2.
%H A002416 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               01-Matrix.html">01-Matrix</a>
%F A002416 G.f. satisfies: A(x) = 1 + 2x*A(4x). [From Paul D. Hanna (pauldhanna(AT)juno.com), 
               Dec 04 2009]
%p A002416 with(finance):seq(mul(futurevalue(2,3,k),k=0..n),n=-1..12); - Zerinvary 
               Lajos (zerinvarylajos(AT)yahoo.com), Jun 30 2008
%t A002416 a[n_]:=2^(n^2); [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Dec 
               13 2008]
%o A002416 (PARI) a(n)=polresultant((x-1)^n,(x+1)^n,x) (from R. Stephan)
%Y A002416 Bisection of A060656.
%Y A002416 Sequence in context: A012393 A063387 A063391 this_sequence A013028 A136632 
               A012919
%Y A002416 Adjacent sequences: A002413 A002414 A002415 this_sequence A002417 A002418 
               A002419
%K A002416 nonn,easy,new
%O A002416 0,2
%A A002416 N. J. A. Sloane (njas(AT)research.att.com).

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