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A266760
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Growth series for affine Coxeter group (or affine Weyl group) D_5.
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1
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1, 6, 20, 51, 111, 216, 386, 646, 1026, 1560, 2287, 3251, 4500, 6086, 8066, 10502, 13460, 17011, 21231, 26200, 32002, 38726, 46466, 55320, 65391, 76787, 89620, 104006, 120066, 137926, 157716, 179571, 203631, 230040, 258946, 290502, 324866, 362200, 402671, 446451, 493716, 544646, 599426, 658246, 721300, 788787, 860911, 937880, 1019906
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OFFSET
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0,2
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REFERENCES
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N. Bourbaki, Groupes et Algèbres de Lie, Chap. 4, 5 and 6, Hermann, Paris, 1968. See Chap. VI, Section 4, Problem 10b, page 231, W_a(t).
J. E. Humphreys, Reflection Groups and Coxeter Groups, Cambridge, 1990. See Table 3.1, page 59.
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LINKS
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Index entries for linear recurrences with constant coefficients, signature (4, -6, 4, -1, 0, 0, 1, -4, 6, -4, 1).
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FORMULA
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The growth series for the affine Coxeter group of type D_k (k >= 3) has g.f. = Product_i (1-x^{m_i+1})/((1-x)*(1-x^{m_i})) where the m_i are [1,3,5,...,2k-3,k-1].
Here (k=5) the G.f. is -(1+t)*(t^3+1)*(1+t+t^2+t^3+t^4+t^5+t^6+t^7) / (-1+t^7) / (-1+t)^4.
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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