cp's OEIS Frontend

A169428 Number of reduced words of length n in Coxeter group on 31 generators S_i with relations (S_i)^2 = (S_i S_j)^32 = I.

%I A169428 #11 May 08 2018 01:04:04
%S A169428 1,31,930,27900,837000,25110000,753300000,22599000000,677970000000,
%T A169428 20339100000000,610173000000000,18305190000000000,549155700000000000,
%U A169428 16474671000000000000,494240130000000000000,14827203900000000000000
%N A169428 Number of reduced words of length n in Coxeter group on 31 generators S_i with relations (S_i)^2 = (S_i S_j)^32 = I.
%C A169428 The initial terms coincide with those of A170750, although the two sequences are eventually different.
%C A169428 First disagreement is at index 32, the difference is 465. - _Klaus Brockhaus_, Jun 30 2011
%C A169428 Computed with Magma using commands similar to those used to compute A154638.
%H A169428 <a href="/index/Rec#order_32">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, 29, -435).
%F A169428 G.f.: (t^32 + 2*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^32 - 29*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).
%F A169428 G.f.: (1+2*sum(k=1..31,x^k)+x^32)/(1-29*sum(k=1..31,x^k)+435*x^32).
%Y A169428 Cf. A170750 (G.f.: (1+x)/(1-30*x) ).
%K A169428 nonn
%O A169428 0,2
%A A169428 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009