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A169345 Number of reduced words of length n in Coxeter group on 44 generators S_i with relations (S_i)^2 = (S_i S_j)^30 = I.

%I A169345 #17 May 10 2018 00:13:12
%S A169345 1,44,1892,81356,3498308,150427244,6468371492,278139974156,
%T A169345 11960018888708,514280812214444,22114074925221092,950905221784506956,
%U A169345 40888924536733799108,1758223755079553361644,75603621468420794550692
%N A169345 Number of reduced words of length n in Coxeter group on 44 generators S_i with relations (S_i)^2 = (S_i S_j)^30 = I.
%C A169345 The initial terms coincide with those of A170763, although the two sequences are eventually different.
%C A169345 First disagreement at index 30: a(30) = 10328515088516010583734507189289051903638876668146, A170763(30) = 10328515088516010583734507189289051903638876669092. - _Klaus Brockhaus_, Jun 23 2011
%C A169345 Computed with Magma using commands similar to those used to compute A154638.
%H A169345 Robert Israel, <a href="/A169345/b169345.txt">Table of n, a(n) for n = 0..600</a>
%H A169345 <a href="/index/Rec#order_30">Index entries for linear recurrences with constant coefficients</a>, signature (42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, -903).
%F A169345 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)/(903*t^30 - 42*t^29 - 42*t^28 - 42*t^27 - 42*t^26 - 42*t^25 - 42*t^24 - 42*t^23 - 42*t^22 - 42*t^21 - 42*t^20 - 42*t^19 - 42*t^18 - 42*t^17 - 42*t^16 - 42*t^15 - 42*t^14 - 42*t^13 - 42*t^12 - 42*t^11 - 42*t^10 - 42*t^9 - 42*t^8 - 42*t^7 - 42*t^6 - 42*t^5 - 42*t^4 - 42*t^3 - 42*t^2 - 42*t + 1).
%p A169345 g:= (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)/(903*t^30 - 42*t^29 - 42*t^28 - 42*t^27 - 42*t^26 - 42*t^25 - 42*t^24 - 42*t^23 - 42*t^22 - 42*t^21 - 42*t^20 - 42*t^19 - 42*t^18 - 42*t^17 - 42*t^16 - 42*t^15 - 42*t^14 - 42*t^13 - 42*t^12 - 42*t^11 - 42*t^10 - 42*t^9 - 42*t^8 - 42*t^7 - 42*t^6 - 42*t^5 - 42*t^4 - 42*t^3 - 42*t^2 - 42*t + 1):
%p A169345 S:= series(g,t,101):
%p A169345 seq(coeff(S,t,j),j=0..100); # _Robert Israel_, Nov 23 2015
%t A169345 coxG[{30,903,-42}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Jan 25 2015 *)
%Y A169345 Cf. A170763 (g.f.: (1+x)/(1-43*x)).
%K A169345 nonn
%O A169345 0,2
%A A169345 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009