cp's OEIS Frontend

A169380 Number of reduced words of length n in Coxeter group on 31 generators S_i with relations (S_i)^2 = (S_i S_j)^31 = I.

%I A169380 #15 Oct 11 2024 06:58:15
%S A169380 1,31,930,27900,837000,25110000,753300000,22599000000,677970000000,
%T A169380 20339100000000,610173000000000,18305190000000000,549155700000000000,
%U A169380 16474671000000000000,494240130000000000000,14827203900000000000000
%N A169380 Number of reduced words of length n in Coxeter group on 31 generators S_i with relations (S_i)^2 = (S_i S_j)^31 = I.
%C A169380 The initial terms coincide with those of A170750, although the two sequences are eventually different.
%C A169380 First disagreement at index 31: a(31) = 6382625094934118999999999999999999999999999535, A170750(31) = 6382625094934119000000000000000000000000000000. - _Klaus Brockhaus_, Jun 17 2011
%C A169380 Computed with Magma using commands similar to those used to compute A154638.
%H A169380 <a href="/index/Rec#order_31">Index entries for linear recurrences with constant coefficients</a>, signature (29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, -435).
%F A169380 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)/(435*t^31 - 29*t^30 - 29*t^29 - 29*t^28 - 29*t^27 - 29*t^26 - 29*t^25 - 29*t^24 - 29*t^23 - 29*t^22 - 29*t^21 - 29*t^20 - 29*t^19 - 29*t^18 - 29*t^17 - 29*t^16 - 29*t^15 - 29*t^14 - 29*t^13 - 29*t^12 - 29*t^11 - 29*t^10 - 29*t^9 - 29*t^8 - 29*t^7 - 29*t^6 - 29*t^5 - 29*t^4 - 29*t^3 - 29*t^2 - 29*t + 1).
%t A169380 coxG[{31,435,-29}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Dec 16 2014 *)
%Y A169380 Cf. A170750 (G.f.: (1+x)/(1-30*x)).
%K A169380 nonn
%O A169380 0,2
%A A169380 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009