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%I #9 Sep 19 2018 06:18:23
%S 0,0,1,1,1,1,2,2,2,3,6,5,5,8,14,15,15,24,27,38,47,58,66,83,92,118,156,
%T 187,234,262,329,367,446,517,657,712,890,1041,1270,1411,1751,1951,
%U 2350,2678,3278,3715
%N a(n) is the number of integer partitions of n for which the crank is equal to the index of the seaweed algebra formed by the integer partition paired with its weight.
%C The index of a Lie algebra, g, is an invariant of the Lie algebra defined by min(dim(Ker(B_f)) where the min is taken over all linear functionals f on g and B_f denotes the bilinear form f([_,_]) were [,] denotes the bracket multiplication on g.
%C For seaweed subalgebras of sl(n), which are Lie subalgebras of sl(n) whose matrix representations are parametrized by an ordered pair of compositions of n, the index can be determined from a corresponding graph called a meander.
%C a(n)>0 for n>2. To see this: if n=k+1 take the partition (k,1).
%H V. Coll, M. Hyatt, C. Magnant, H. Wang, <a href="http://dx.doi.org/10.4172/1736-4337.1000227">Meander graphs and Frobenius seaweed Lie algebras II</a>, Journal of Generalized Lie Theory and Applications 9 (1) (2015) 227.
%H V. Dergachev, A. Kirillov, <a href="https://www.emis.de/journals/JLT/vol.10_no.2/6.html">Index of Lie algebras of seaweed type</a>, J. Lie Theory 10 (2) (2000) 331-343.
%Y Cf. A237832, A318176, A318177, A318178, A318196, A318203
%K nonn,more
%O 1,7
%A _Nick Mayers_, _Melissa Mayers_, Aug 21 2018
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