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A234598
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Cardinality of the Weyl alternation set corresponding to the zero-weight in the adjoint representation of the Lie algebra of so(2n).
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0
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9, 18, 35, 82, 180, 385, 846, 1853, 4034, 8810, 19249, 42014, 91727, 200298, 437316, 954809, 2084746, 4551801, 9938290, 21699138, 47377577, 103443386, 225856667, 493131922, 1076696324, 2350841633, 5132790390, 11206852917, 24468864530
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OFFSET
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4,1
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COMMENTS
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Cardinality of the Weyl alternation set corresponding to the zero-weight in the adjoint representation of the Lie algebra of type D and rank n.
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LINKS
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FORMULA
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G.f.: x^4*(2*x^3 + 8*x^2 + 9*x + 9)/(-x^4 - 3*x^3 - x^2 - x + 1). - Ralf Stephan, Jan 05 2014
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EXAMPLE
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For n = 8, a(n) = 107+73 = 180 and a(n) = 3(34) + 2(14) + 6(7) + 2(4) = 180.
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MAPLE
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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 9:
elif n=5 then return 18:
elif n=6 then return 35:
elif n=5 then return 82:
else return
3*r(n-1)+2*r(n-2)+6*r(n-3)+2*r(n-4):
end if;
end proc:
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MATHEMATICA
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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