Search: id:A123290
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%I A123290
%S A123290 2,8,36,156,652,2668,10796,43436,174252,698028,2794156,11180716,
%T A123290 44731052,178940588,715795116,2863245996,11453115052,45812722348,
%U A123290 183251413676,733006703276,2932028910252,11728119835308,46912487729836
%N A123290 Number of distinct C(n,2)-tuples of zeros and ones that are obtained 
               as the collection of all 2 X 2 minor determinants of a 2 X n matrix 
               over GF(2).
%C A123290 Or, the number of commutators in a central extension of order 2^C(n+1,
               2) covering the elementary Abelian 2-group of order 2^n. Probably 
               also equal to the number of symmetric (n-1)-by-(n-1) matrices with 
               entries in GF(2) of rank less than or equal to 2 and the number of 
               skew-symmetric n-by-n matrices in GF(2) of rank less than or equal 
               to 2.
%D A123290 Luise-Charlotte Kappe and Robert F. Morse, On Commutators in groups. 
               To appear in the Proceedings of Groups St. Andrews 2005 LMS Lecture 
               Series.
%F A123290 a(n) = (2^(2n-1) - 2^n - 2^(n-1) + 4)/3 = 1 + (2^n - 1)*(2^(n-1) - 1)/
               3
%e A123290 a(4) = 36. Let G be a central extension of order 2^C(5,2) covering (Z/
               2Z)^4; the commutator subgroup of G has order 2^C(4,2) = 64, so it 
               is not the case that every element of the commutator subgroup of 
               G is actually a commutator.
%o A123290 (MAGMA) minors := function(n) F := GF(2); V := VectorSpace(F,2*n); S 
               := { } ; for v in V do M := Matrix(F,2,n,ElementToSequence(v)); seq 
               := Minors(M,2); S := Include(S,seq); end for; return #S; end function;
%Y A123290 Sequence in context: A007508 A122674 A076122 this_sequence A088675 A027743 
               A152124
%Y A123290 Adjacent sequences: A123287 A123288 A123289 this_sequence A123291 A123292 
               A123293
%K A123290 nonn
%O A123290 2,1
%A A123290 David Savitt (savitt(AT)math.arizona.edu), Oct 10 2006, Oct 12 2006

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