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A169420 Number of reduced words of length n in Coxeter group on 23 generators S_i with relations (S_i)^2 = (S_i S_j)^32 = I.

%I A169420 #12 May 08 2018 00:59:42
%S A169420 1,23,506,11132,244904,5387888,118533536,2607737792,57370231424,
%T A169420 1262145091328,27767192009216,610878224202752,13439320932460544,
%U A169420 295665060514131968,6504631331310903296,143101889288839872512
%N A169420 Number of reduced words of length n in Coxeter group on 23 generators S_i with relations (S_i)^2 = (S_i S_j)^32 = I.
%C A169420 The initial terms coincide with those of A170742, although the two sequences are eventually different.
%C A169420 First disagreement is at index 32, the difference is 253. - _Klaus Brockhaus_, Jun 27 2011
%C A169420 Computed with Magma using commands similar to those used to compute A154638.
%H A169420 <a href="/index/Rec#order_32">Index entries for linear recurrences with constant coefficients</a>, signature (21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, -231).
%F A169420 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)/(231*t^32 - 21*t^31 - 21*t^30 - 21*t^29 - 21*t^28 - 21*t^27 - 21*t^26 - 21*t^25 - 21*t^24 - 21*t^23 - 21*t^22 - 21*t^21 - 21*t^20 - 21*t^19 - 21*t^18 - 21*t^17 - 21*t^16 - 21*t^15 - 21*t^14 - 21*t^13 - 21*t^12 - 21*t^11 - 21*t^10 - 21*t^9 - 21*t^8 - 21*t^7 - 21*t^6 - 21*t^5 - 21*t^4 - 21*t^3 - 21*t^2 - 21*t + 1).
%F A169420 G.f.: (1+2*sum(k=1..31, x^k)+x^32)/(1-21*sum(k=1..31, x^k)+231*x^32).
%Y A169420 Cf. A170742 (G.f.: (1+x)/(1-22*x) ).
%K A169420 nonn
%O A169420 0,2
%A A169420 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009