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1, 2, 16, 512, 65536, 33554432, 68719476736, 562949953421312, 18446744073709551616, 2417851639229258349412352, 1267650600228229401496703205376, 2658455991569831745807614120560689152, 22300745198530623141535718272648361505980416, 748288838313422294120286634350736906063837462003712
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OFFSET
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0,2
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COMMENTS
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For n >= 1 a(n) is the number of n X n (0,1) matrices.
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, Sep 27 2007
Hankel transform of A064062 . - Philippe DELEHAM, Nov 19 2007
a(n) is also the order of the semigroup (monoid) of all binary relations on an n-set. [From Abdullahi Umar, Sep 14 2008]
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REFERENCES
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F. Harary and R. W. Robinson, Labeled bipartite blocks, Canad. J. Math., 31 (1979), 60-68.
Kent E. Morrison, Integer Sequences and Matrices Over Finite Fields, Journal of Integer Sequences, Vol. 9 (2006), Article 06.2.1.
Howie, J. M. Fundamentals of semigroup theory. Oxford: Clarendon Press, (1995). [From Abdullahi Umar, Sep 14 2008]
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 0..33
P. J. Cameron, Sequences realized by oligomorphic permutation groups, J. Integ. Seqs. Vol. 3 (2000), #00.1.5.
T. Eisenkoelbl, 2-Enumerations of halved alternating sign matrices.
T. Eisenk\"olbl, 2-Enumerations of halved alternating sign matrices
Daniele A. Gewurz and Francesca Merola, Sequences realized as Parker vectors ..., J. Integer Seqs., Vol. 6, 2003.
G. Pfeiffer, Counting Transitive Relations, Journal of Integer Sequences, Vol. 7 (2004), Article 04.3.2.
Eric Weisstein's World of Mathematics, 01-Matrix
Index to divisibility sequences
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FORMULA
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G.f. satisfies: A(x) = 1 + 2*x*A(4x). [From Paul D. Hanna, Dec 04 2009]
2^n * Sum_i=0...C(n,2);C(C(n,2),i)*3^i. The summation conditions on i,0<=i<=C(n,2), the number of 1's above the main diagonal in the matrix representations of the relations on {1,2,...,n}. [From Geoffrey Critzer, 18 Feb 2011]
G.f.: 1 / (1 - 2^1*x / (1 - 2^1*(2^2-1)*x / (1 - 2^5 * x / (1 - 2^3*(2^4-1)*x / (1 - 2^9*x / (1 - 2^5*(2^6-1)*x / ...)))))). - Michael Somos, May 12 2012
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EXAMPLE
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1 + 2*x + 16*x^2 + 512*x^3 + 65536*x^4 + 33554432*x^5 + ...
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MATHEMATICA
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a[n_]:=2^(n^2); [From Vladimir Orlovsky, Dec 13 2008]
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PROG
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(PARI) a(n)=polresultant((x-1)^n, (x+1)^n, x) (from R. Stephan)
(MAGMA) [2^(n^2): n in [0..15]]; // Vincenzo Librandi, May 13 2011
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CROSSREFS
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Bisection of A060656. Cf. also A064231.
Sequence in context: A189152 A063387 A063391 * A013028 A136632 A168405
Adjacent sequences: A002413 A002414 A002415 * A002417 A002418 A002419
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane.
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STATUS
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approved
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