A243094 Cardinality of the Weyl alternation set corresponding to the zero-weight in the representation of the Lie algebra sp(2n) whose highest weight is the second fundamental weight.
1, 2, 5, 8, 19, 44, 92, 201, 444, 965, 2104, 4602, 10045, 21924, 47879, 104540, 228236, 498337, 1088072, 2375657, 5186976, 11325186, 24727205, 53988976, 117878715, 257374492, 561947340, 1226946953, 2678896484, 5849059949, 12770744632, 27883440986, 60880261949
Offset: 0
Keywords
Links
- P. E. Harris, Combinatorial problems related to Kostant's weight multiplicity formula, PhD Dissertation, University of Wisconsin-Milwaukee, 2012.
- 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 [math.RT], 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).
Crossrefs
Cf. A232162.
Programs
-
Maple
r:=proc(n::nonnegint) option remember if n=0 then return 0: elif n=1 then return 0: elif n=2 then return 2: elif n=3 then return 3: 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=0 then return 0: elif n=1 then return 1: else return r(n)+r(n-1): end if; end proc:
-
Mathematica
Join[{1}, LinearRecurrence[{1, 1, 3, 1}, {2, 5, 8, 19}, 32]] (* Jean-François Alcover, Dec 05 2017 *) -
PARI
Vec( (x^4+2*x^3-2*x^2-x-1) / (x^4+3*x^3+x^2+x-1) +O(x^66) ) \\ Joerg Arndt, Aug 18 2014
Formula
a(n) = a(n-1) + a(n-2) + 3*a(n-3) + a(n-4).
G.f.: (x^4 + 2*x^3 - 2*x^2 - x - 1) / (x^4 + 3*x^3 + x^2 + x - 1). - Joerg Arndt, Aug 18 2014
Comments