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 A167148 Number of reduced words of length n in Coxeter group on 20 generators S_i with relations (S_i)^2 = (S_i S_j)^14 = I. 1
 1, 20, 380, 7220, 137180, 2606420, 49521980, 940917620, 17877434780, 339671260820, 6453753955580, 122621325156020, 2329805177964380, 44266298381323220, 841059669245140990, 15980133715657675200 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS The initial terms coincide with those of A170739, although the two sequences are eventually different. Computed with MAGMA using commands similar to those used to compute A154638. LINKS G. C. Greubel, Table of n, a(n) for n = 0..500 Index entries for linear recurrences with constant coefficients, signature (18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, -171). FORMULA G.f.: (t^14 + 2*t^13 + 2*t^12 + 2*t^11 + 2*t^10 + 2*t^9 + 2*t^8 + 2*t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(171*t^14 - 18*t^13 - 18*t^12 - 18*t^11 - 18*t^10 - 18*t^9 - 18*t^8 - 18*t^7 - 18*t^6 - 18*t^5 - 18*t^4 - 18*t^3 - 18*t^2 - 18*t + 1). MATHEMATICA With[{num=Total[2t^Range[13]]+t^14+1, den=Total[-18 t^Range[13]]+ 171t^14+ 1}, CoefficientList[Series[num/den, {t, 0, 30}], t]] (* Harvey P. Dale, Sep 15 2011 *) CoefficientList[Series[(t^14 + 2*t^13 + 2*t^12 + 2*t^11 + 2*t^10 + 2*t^9 + 2*t^8 + 2*t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/ (171*t^14 - 18*t^13 - 18*t^12 - 18*t^11 - 18*t^10 - 18*t^9 - 18*t^8 - 18*t^7 - 18*t^6 - 18*t^5 - 18*t^4 - 18*t^3 - 18*t^2 - 18*t + 1), {t, 0, 50}], t] (* G. C. Greubel, Jun 04 2016 *) CROSSREFS Sequence in context: A166414 A166601 A167073 * A167680 A167931 A168697 Adjacent sequences: A167145 A167146 A167147 * A167149 A167150 A167151 KEYWORD nonn AUTHOR John Cannon and N. J. A. Sloane, Dec 03 2009 STATUS approved

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Last modified June 17 06:41 EDT 2024. Contains 373432 sequences. (Running on oeis4.)