OFFSET
3,1
COMMENTS
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([_,_]), where [,] denotes the bracket multiplication on g.
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.
LINKS
Vincent Coll, et al., Meander graphs and Frobenius seaweed Lie algebras II, Journal of Generalized Lie Theory and Applications 9.1 (2015).
Vladimir Dergachev, and Alexandre Kirillov, Index of Lie algebras of seaweed type, J. Lie Theory 10.2 (2000): 331-343.
Index entries for linear recurrences with constant coefficients, signature (6,-12,8)
FORMULA
a(n) = (7*n-15)*2^(n-3) for 3 <= n <= 5 and a(n) = ((1/2)*n^2+(11/4)*n-(25/4))*2^(n-3) for n >= 5.
G.f.: 2*x^3*(3-5x-2x^2+5x^3-2x^4)/(1-2*x)^3. [Corrected by Georg Fischer, May 23 2019]
E.g.f.: (75 + 72*x - 30*x^2 - 8*x^3 + 2*x^4 - 3*exp(2*x)*(25 - 26*x - 8*x^2))/96. - Stefano Spezia, Nov 16 2022
MATHEMATICA
CoefficientList[Series[2*x^3*(3-5x-2x^2+5x^3-2x^4)/(1-2*x)^3, {x, 0, 33}], x] (* Georg Fischer, May 23 2019 *)
PROG
(Sage)
[(7*n-15)*2^(n-3) if n < 5 else ((1/2)*n^2+(11/4)*n-(25/4))*2^(n-3) for n in range(3, 263)]
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Nick Mayers, Andrew W. Mayers, Jun 25 2018
STATUS
approved