# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a167183 Showing 1-1 of 1 %I A167183 #12 Dec 16 2018 19:55:11 %S A167183 1,24,552,12696,292008,6716184,154472232,3552861336,81715810728, %T A167183 1879463646744,43227663875112,994236269127576,22867434189934248, %U A167183 525950986368487704,12096872686475216916,278228071788929982720 %N A167183 Number of reduced words of length n in Coxeter group on 24 generators S_i with relations (S_i)^2 = (S_i S_j)^14 = I. %C A167183 The initial terms coincide with those of A170743, although the two sequences are eventually different. %C A167183 Computed with MAGMA using commands similar to those used to compute A154638. %H A167183 G. C. Greubel, Table of n, a(n) for n = 0..500 %H A167183 Index entries for linear recurrences with constant coefficients, signature (22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, -253). %F A167183 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)/(253*t^14 - 22*t^13 - 22*t^12 - 22*t^11 - 22*t^10 - 22*t^9 - 22*t^8 - 22*t^7 - 22*t^6 - 22*t^5 - 22*t^4 - 22*t^3 - 22*t^2 - 22*t + 1). %t A167183 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)/ (253*t^14 - 22*t^13 - 22*t^12 - 22*t^11 - 22*t^10 - 22*t^9 - 22*t^8 - 22*t^7 - 22*t^6 - 22*t^5 - 22*t^4 - 22*t^3 - 22*t^2 - 22*t + 1), {t, 0, 50}], t] (* _G. C. Greubel_, Jun 04 2016 *) %t A167183 coxG[{14,253,-22}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Dec 16 2018 *) %K A167183 nonn %O A167183 0,2 %A A167183 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE