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A266766
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Growth series for affine Coxeter group (or affine Weyl group) D_11.
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1
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1, 12, 77, 353, 1298, 4070, 11298, 28468, 66275, 144430, 297585, 584255, 1099879, 1995478, 3503742, 5974816, 9924564, 16098676, 25556652, 39780455, 60813480, 91436445, 135387879, 197638068, 284726628, 405175311, 569989222, 793261337, 1092897070, 1491477647, 2017283215, 2705498950, 3599629936, 4753153273, 6231438741, 8113972406
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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 (8, -28, 55, -62, 28, 27, -54, 27, 27, -54, 27, 27, -53, 19, 56, -117, 118, -64, 10, -10, 63, -110, 89, -1, -81, 81, 0, -82, 89, -29, -18, -11, 99, -173, 173, -99, 11, 18, 29, -89, 82, 0, -81, 81, 1, -89, 110, -63, 10, -10, 64, -118, 117, -56, -19, 53, -27, -27, 54, -27, -27, 54, -27, -28, 62, -55, 28, -8, 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].
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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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