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A234597 Number of Weyl group elements, not containing an s_1 factor, 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
5, 11, 21, 48, 107, 229, 501, 1099, 2394, 5225, 11417, 24923, 54409, 118808, 259403, 566361, 1236597, 2699975, 5895058, 12871185, 28102765, 61359099, 133970477, 292509056, 638659595, 1394439181, 3044596421, 6647523443, 14514097002, 31689848889, 69191112641 (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. USA, 44 (No. 6, June 1958), 588-589.

Index entries for linear recurrences with constant coefficients, signature (1,1,3,1).

FORMULA

a(n) = A234576(n) + A234576(n-1).

a(n) = a(n-1)+a(n-2)+3*a(n-3)+a(n-4). G.f.: -x^4*(x^3+5*x^2+6*x+5) / (x^4+3*x^3+x^2+x-1). - Colin Barker, Dec 30 2013

EXAMPLE

For n=6, a(6) = A234576(6) + A234576(5)= 14+7 = 21.

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 5:

elif n=5 then return 11:

else return

r(n)+r(n-1):

end if;

end proc:

MATHEMATICA

LinearRecurrence[{1, 1, 3, 1}, {5, 11, 21, 48}, 40] (* Harvey P. Dale, Feb 17 2016 *)

PROG

(PARI) Vec(-x^4*(x^3+5*x^2+6*x+5)/(x^4+3*x^3+x^2+x-1) + O(x^100)) \\ Colin Barker, Dec 30 2013

CROSSREFS

Cf. A234576.

Sequence in context: A163704 A131898 A168642 * A261982 A296033 A296968

Adjacent sequences:  A234594 A234595 A234596 * A234598 A234599 A234600

KEYWORD

nonn,easy

AUTHOR

Erik Insko, Dec 28 2013

STATUS

approved

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Last modified May 31 18:34 EDT 2020. Contains 334748 sequences. (Running on oeis4.)