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 A234598 Cardinality of the Weyl alternation set corresponding to the zero-weight in the adjoint representation of the Lie algebra of so(2n). 0
 9, 18, 35, 82, 180, 385, 846, 1853, 4034, 8810, 19249, 42014, 91727, 200298, 437316, 954809, 2084746, 4551801, 9938290, 21699138, 47377577, 103443386, 225856667, 493131922, 1076696324, 2350841633, 5132790390, 11206852917, 24468864530 (list; graph; refs; listen; history; text; internal format)
 OFFSET 4,1 COMMENTS Cardinality of the Weyl alternation set corresponding to the zero-weight in the adjoint representation of the Lie algebra of type D and rank n. REFERENCES P. E. Harris, Combinatorial problems related to Kostant's weight multiplicity formula, PhD Dissertation, University of Wisconsin-Milwaukee, 2012. LINKS P. E. Harris, E. Insko, L. K. Williams, The adjoint representation of a Lie algebra and the support of Kostant's weight multiplicity formula, arXiv preprint arXiv:1401.0055, 2013 B. Kostant, A Formula for the Multiplicity of a Weight, Proc Natl Acad Sci U S A. 1958 June; 44(6): 588-589. Index entries for linear recurrences with constant coefficients, signature (1,1,3,1). FORMULA a(n) = A234597(n) + A234576(n). a(n) = 3*A234576(n-1) + 2*A234576(n-2) + 6*A234576(n-3) + 2*A234576(n-4). G.f.: x^4*(2*x^3 + 8*x^2 + 9*x + 9)/(-x^4 - 3*x^3 - x^2 - x + 1). - Ralf Stephan, Jan 05 2014 EXAMPLE For n = 8, a(n) = 107+73 = 180 and a(n) = 3(34) + 2(14) + 6(7) + 2(4) = 180. MAPLE r:=proc(n::nonnegint) if n<=3 then return 0: elif n=4 then return 4: elif n=5 then return 7: elif n=6 then return 14: elif n=7 then return 34: else return r(n-1)+r(n-2)+3*r(n-3)+r(n-4): end if; end proc: a:=proc(n::nonnegint) if n<=3 then return 0: elif n=4 then return 9: elif n=5 then return 18: elif n=6 then return 35: elif n=5 then return 82: else return 3*r(n-1)+2*r(n-2)+6*r(n-3)+2*r(n-4): end if; end proc: MATHEMATICA LinearRecurrence[{1, 1, 3, 1}, {9, 18, 35, 82}, 30] (* Jean-François Alcover, Dec 06 2017 *) CROSSREFS Cf. A232163, A232165, A234576, A234597. Sequence in context: A139591 A191268 A109668 * A051063 A173942 A162689 Adjacent sequences:  A234595 A234596 A234597 * A234599 A234600 A234601 KEYWORD nonn,easy AUTHOR Erik Insko, Dec 28 2013 EXTENSIONS More terms from Ralf Stephan, Jan 05 2014 STATUS approved

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Last modified January 27 04:57 EST 2020. Contains 331291 sequences. (Running on oeis4.)