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A168797 Number of reduced words of length n in Coxeter group on 24 generators S_i with relations (S_i)^2 = (S_i S_j)^19 = I.

%I A168797 #16 Feb 09 2025 14:27:55
%S A168797 1,24,552,12696,292008,6716184,154472232,3552861336,81715810728,
%T A168797 1879463646744,43227663875112,994236269127576,22867434189934248,
%U A168797 525950986368487704,12096872686475217192,278228071788929995416
%N A168797 Number of reduced words of length n in Coxeter group on 24 generators S_i with relations (S_i)^2 = (S_i S_j)^19 = I.
%C A168797 The initial terms coincide with those of A170743, although the two sequences are eventually different.
%C A168797 First disagreement at index 19: a(19) = 77859621837485958847208580, A170743(19) = 77859621837485958847208856. - _Klaus Brockhaus_, Apr 01 2011
%C A168797 Computed with MAGMA using commands similar to those used to compute A154638.
%H A168797 G. C. Greubel, <a href="/A168797/b168797.txt">Table of n, a(n) for n = 0..500</a>
%H A168797 <a href="/index/Rec#order_19">Index entries for linear recurrences with constant coefficients</a>, signature (22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, -253).
%F A168797 G.f.: (t^19 + 2*t^18 + 2*t^17 + 2*t^16 + 2*t^15 + 2*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^19 - 22*t^18 - 22*t^17 - 22*t^16 - 22*t^15 - 22*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 A168797 CoefficientList[Series[(t^19 + 2*t^18 + 2*t^17 + 2*t^16 + 2*t^15 + 2*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^19 - 22*t^18 - 22*t^17 - 22*t^16 - 22*t^15 - 22*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_, Aug 16 2016 *)
%t A168797 coxG[{19,253,-22}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Feb 09 2025 *)
%Y A168797 Cf. A170743 (G.f.: (1+x)/(1-23*x)).
%K A168797 nonn
%O A168797 0,2
%A A168797 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009