The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

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