%I
%S 1,4,6,14,20,43,59,108,158,265,373,600,838,1301,1797,2693,3695,5379,
%T 7291,10407,14023,19651,26227,36166,47888,65193,85731,115308,150598,
%U 200420
%N Number of isomorphism classes of linking pairings on finite Abelian 2groups of fixed order 2^n.
%C A linking pairing on a finite Abelian group G is a nonsingular symmetric bilinear form G x G > Q/Z.
%C The combinatorics of this sequence are surprisingly complicated. The corresponding case when p is odd is easier and is now understood. The sequence is a combinatorial refinement of partitions of integers.
%D F. Deloup, Monoide des enlacements et facteurs orthogonaux, Algebraic and Geometric Topology, 5 (2005) 419442.
%D A. Kawauchi and S. Kojima, Algebraic classification of linking pairings on 3manifolds, Math. Ann. 253 (1980), 2942.
%H F. Deloup, <a href="http://www.msp.warwick.ac.uk/agt/2005/05/p019.xhtml">Monoide des enlacements et facteurs orthogonaux</a>.
%H F. Deloup, <a href="/A122555/a122555.txt">Maple program</a>
%e a(2) = 4 because there are 4 nonequivalent linking pairings on finite Abelian groups of order 2^2 = 4: there are two nonequivalent cyclic pairings on Z/4, one direct product of two cyclic pairings on Z/2 and one noncyclic pairing on Z/2 x Z/2.
%K nonn
%O 1,2
%A Florian Deloup (deloup(AT)math.upstlse.fr), Sep 20 2006
