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%I #12 Nov 24 2016 10:29:42
%S 1,24,552,12696,292008,6716184,154472232,3552861336,81715810728,
%T 1879463646744,43227663875112,994236269127576,22867434189934248,
%U 525950986368487428,12096872686475204496,278228071788929557680
%N Number of reduced words of length n in Coxeter group on 24 generators S_i with relations (S_i)^2 = (S_i S_j)^13 = I.
%C The initial terms coincide with those of A170743, although the two sequences are eventually different.
%C Computed with MAGMA using commands similar to those used to compute A154638.
%H G. C. Greubel, <a href="/A167077/b167077.txt">Table of n, a(n) for n = 0..500</a>
%H <a href="/index/Rec#order_13">Index entries for linear recurrences with constant coefficients</a>, signature (22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, -253).
%F G.f.: (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^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 CoefficientList[Series[(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^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_, May 31 2016 *)
%t coxG[{13,253,-22}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Nov 04 2016 *)
%K nonn
%O 0,2
%A _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009
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