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A169390 Number of reduced words of length n in Coxeter group on 41 generators S_i with relations (S_i)^2 = (S_i S_j)^31 = I.

%I A169390 #26 Oct 11 2024 23:02:55
%S A169390 1,41,1640,65600,2624000,104960000,4198400000,167936000000,
%T A169390 6717440000000,268697600000000,10747904000000000,429916160000000000,
%U A169390 17196646400000000000,687865856000000000000,27514634240000000000000
%N A169390 Number of reduced words of length n in Coxeter group on 41 generators S_i with relations (S_i)^2 = (S_i S_j)^31 = I.
%C A169390 The initial terms coincide with those of A170760, although the two sequences are eventually different.
%C A169390 First disagreement at index 31: a(31) = 47269781688880726015999999999999999999999999999180, A170760(31) = 47269781688880726016000000000000000000000000000000. - _Klaus Brockhaus_, Jun 17 2011
%C A169390 Computed with Magma using commands similar to those used to compute A154638.
%H A169390 Vincenzo Librandi, <a href="/A169390/b169390.txt">Table of n, a(n) for n = 0..100</a>
%H A169390 <a href="/index/Rec#order_31">Index entries for linear recurrences with constant coefficients</a>, signature (39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, -780).
%F A169390 G.f.: (t^31 + 2*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)/(780*t^31 - 39*t^30 - 39*t^29 - 39*t^28 - 39*t^27 - 39*t^26 - 39*t^25 - 39*t^24 - 39*t^23 - 39*t^22 - 39*t^21 - 39*t^20 - 39*t^19 - 39*t^18 - 39*t^17 - 39*t^16 - 39*t^15 - 39*t^14 - 39*t^13 - 39*t^12 - 39*t^11 - 39*t^10 - 39*t^9 - 39*t^8 - 39*t^7 - 39*t^6 - 39*t^5 - 39*t^4 - 39*t^3 - 39*t^2 - 39*t + 1).
%t A169390 With[{num=Total[2t^Range[30]]+t^31+1,den=Total[-39 t^Range[30]]+780 t^31+ 1}, CoefficientList[Series[num/den,{t,0,30}],t]] (* _Harvey P. Dale_, Feb 04 2012 *)
%Y A169390 Cf. A170760 (G.f.: (1+x)/(1-40*x)).
%K A169390 nonn
%O A169390 0,2
%A A169390 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009