OFFSET
4,1
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, and 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) = 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
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
KEYWORD
nonn,easy
AUTHOR
Erik Insko, Dec 28 2013
STATUS
approved