cp's OEIS Frontend

A169325 Number of reduced words of length n in Coxeter group on 24 generators S_i with relations (S_i)^2 = (S_i S_j)^30 = I.

%I A169325 #12 May 10 2018 00:21:56
%S A169325 1,24,552,12696,292008,6716184,154472232,3552861336,81715810728,
%T A169325 1879463646744,43227663875112,994236269127576,22867434189934248,
%U A169325 525950986368487704,12096872686475217192,278228071788929995416
%N A169325 Number of reduced words of length n in Coxeter group on 24 generators S_i with relations (S_i)^2 = (S_i S_j)^30 = I.
%C A169325 The initial terms coincide with those of A170743, although the two sequences are eventually different.
%C A169325 First disagreement at index 30: a(30) = 74185407434244900547189100124961040137236, A170743(30) = 74185407434244900547189100124961040137512. - _Klaus Brockhaus_, Jun 22 2011
%C A169325 Computed with Magma using commands similar to those used to compute A154638.
%H A169325 <a href="/index/Rec#order_30">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, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, -253).
%F A169325 G.f.: (t^30 + 2*t^29 + 2*t^28 + 2*t^27 + 2*t^26 + 2*t^25 + 2*t^24 + 2*t^23 + 2*t^22 + 2*t^21 + 2*t^20 + 2*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^30 - 22*t^29 - 22*t^28 - 22*t^27 - 22*t^26 - 22*t^25 - 22*t^24 - 22*t^23 - 22*t^22 - 22*t^21 - 22*t^20 - 22*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 A169325 With[{num=Total[2t^Range[29]]+t^30+1,den=Total[-22 t^Range[29]]+253t^30+ 1},CoefficientList[Series[num/den,{t,0,30}],t]] (* _Harvey P. Dale_, Mar 06 2013 *)
%Y A169325 Cf. A170743 (G.f.: (1+x)/(1-23*x)).
%K A169325 nonn
%O A169325 0,2
%A A169325 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009