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A170485 Number of reduced words of length n in Coxeter group on 44 generators S_i with relations (S_i)^2 = (S_i S_j)^45 = I.

%I A170485 #8 Jun 11 2024 13:44:45
%S A170485 1,44,1892,81356,3498308,150427244,6468371492,278139974156,
%T A170485 11960018888708,514280812214444,22114074925221092,950905221784506956,
%U A170485 40888924536733799108,1758223755079553361644,75603621468420794550692
%N A170485 Number of reduced words of length n in Coxeter group on 44 generators S_i with relations (S_i)^2 = (S_i S_j)^45 = I.
%C A170485 The initial terms coincide with those of A170763, although the two sequences are eventually different.
%C A170485 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170485 <a href="/index/Rec#order_45">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, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, -903).
%F A170485 G.f. (t^45 + 2*t^44 + 2*t^43 + 2*t^42 + 2*t^41 + 2*t^40 + 2*t^39 + 2*t^38 +
%F A170485 2*t^37 + 2*t^36 + 2*t^35 + 2*t^34 + 2*t^33 + 2*t^32 + 2*t^31 + 2*t^30 +
%F A170485 2*t^29 + 2*t^28 + 2*t^27 + 2*t^26 + 2*t^25 + 2*t^24 + 2*t^23 + 2*t^22 +
%F A170485 2*t^21 + 2*t^20 + 2*t^19 + 2*t^18 + 2*t^17 + 2*t^16 + 2*t^15 + 2*t^14 +
%F A170485 2*t^13 + 2*t^12 + 2*t^11 + 2*t^10 + 2*t^9 + 2*t^8 + 2*t^7 + 2*t^6 +
%F A170485 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(903*t^45 - 42*t^44 - 42*t^43 -
%F A170485 42*t^42 - 42*t^41 - 42*t^40 - 42*t^39 - 42*t^38 - 42*t^37 - 42*t^36 -
%F A170485 42*t^35 - 42*t^34 - 42*t^33 - 42*t^32 - 42*t^31 - 42*t^30 - 42*t^29 -
%F A170485 42*t^28 - 42*t^27 - 42*t^26 - 42*t^25 - 42*t^24 - 42*t^23 - 42*t^22 -
%F A170485 42*t^21 - 42*t^20 - 42*t^19 - 42*t^18 - 42*t^17 - 42*t^16 - 42*t^15 -
%F A170485 42*t^14 - 42*t^13 - 42*t^12 - 42*t^11 - 42*t^10 - 42*t^9 - 42*t^8 -
%F A170485 42*t^7 - 42*t^6 - 42*t^5 - 42*t^4 - 42*t^3 - 42*t^2 - 42*t + 1)
%t A170485 coxG[{45,903,-42}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Jun 11 2024 *)
%K A170485 nonn
%O A170485 0,2
%A A170485 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009