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A234576 Number of Weyl group elements, not containing s_1 or s_2, which contribute nonzero terms to Kostant's weight multiplicity formula when computing the multiplicity of the zero-weight in the adjoint representation for the Lie algebra of type D and rank n. 2
4, 7, 14, 34, 73, 156, 345, 754, 1640, 3585, 7832, 17091, 37318, 81490, 177913, 388448, 848149, 1851826, 4043232, 8827953, 19274812, 42084287, 91886190, 200622866, 438036729, 956402452, 2088193969, 4559329474, 9954767528, 21735081361, 47456031280 (list; graph; refs; listen; history; text; internal format)
OFFSET

4,1

REFERENCES

P. E. Harris, Combinatorial problems related to Kostant's weight multiplicity formula, PhD Dissertation, University of Wisconsin-Milwaukee, 2012.

LINKS

Table of n, a(n) for n=4..34.

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) =  a(n-1) + a(n-2) + 3*a(n-3) + a(n-4).

G.f.: -x^4*(x^3+3*x^2+3*x+4) / (x^4+3*x^3+x^2+x-1). - Colin Barker, Dec 30 2013

EXAMPLE

For n = 8, a(8) = 34+14+3*7+4 = 73.

MAPLE

a:=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

a(n-1)+a(n-2)+3*a(n-3)+a(n-4):

end if;

end proc:

MATHEMATICA

LinearRecurrence[{1, 1, 3, 1}, {4, 7, 14, 34}, 31] (* Jean-Fran├žois Alcover, Nov 26 2017 *)

PROG

(PARI) Vec(-x^4*(x^3+3*x^2+3*x+4)/(x^4+3*x^3+x^2+x-1) + O(x^100)) \\ Colin Barker, Dec 30 2013

CROSSREFS

Sequence in context: A245002 A199628 A049945 * A076586 A240266 A064961

Adjacent sequences:  A234573 A234574 A234575 * A234577 A234578 A234579

KEYWORD

nonn,easy

AUTHOR

Erik Insko, Dec 28 2013

STATUS

approved

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Last modified November 12 05:52 EST 2019. Contains 329051 sequences. (Running on oeis4.)