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A170437 Number of reduced words of length n in Coxeter group on 44 generators S_i with relations (S_i)^2 = (S_i S_j)^44 = I.

%I A170437 #8 Jul 09 2017 15:51:15
%S A170437 1,44,1892,81356,3498308,150427244,6468371492,278139974156,
%T A170437 11960018888708,514280812214444,22114074925221092,950905221784506956,
%U A170437 40888924536733799108,1758223755079553361644,75603621468420794550692
%N A170437 Number of reduced words of length n in Coxeter group on 44 generators S_i with relations (S_i)^2 = (S_i S_j)^44 = I.
%C A170437 The initial terms coincide with those of A170763, although the two sequences are eventually different.
%C A170437 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170437 <a href="/index/Rec#order_44">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, -903).
%F A170437 G.f. (t^44 + 2*t^43 + 2*t^42 + 2*t^41 + 2*t^40 + 2*t^39 + 2*t^38 + 2*t^37 +
%F A170437 2*t^36 + 2*t^35 + 2*t^34 + 2*t^33 + 2*t^32 + 2*t^31 + 2*t^30 + 2*t^29 +
%F A170437 2*t^28 + 2*t^27 + 2*t^26 + 2*t^25 + 2*t^24 + 2*t^23 + 2*t^22 + 2*t^21 +
%F A170437 2*t^20 + 2*t^19 + 2*t^18 + 2*t^17 + 2*t^16 + 2*t^15 + 2*t^14 + 2*t^13 +
%F A170437 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
%F A170437 + 2*t^3 + 2*t^2 + 2*t + 1)/(903*t^44 - 42*t^43 - 42*t^42 - 42*t^41 -
%F A170437 42*t^40 - 42*t^39 - 42*t^38 - 42*t^37 - 42*t^36 - 42*t^35 - 42*t^34 -
%F A170437 42*t^33 - 42*t^32 - 42*t^31 - 42*t^30 - 42*t^29 - 42*t^28 - 42*t^27 -
%F A170437 42*t^26 - 42*t^25 - 42*t^24 - 42*t^23 - 42*t^22 - 42*t^21 - 42*t^20 -
%F A170437 42*t^19 - 42*t^18 - 42*t^17 - 42*t^16 - 42*t^15 - 42*t^14 - 42*t^13 -
%F A170437 42*t^12 - 42*t^11 - 42*t^10 - 42*t^9 - 42*t^8 - 42*t^7 - 42*t^6 - 42*t^5
%F A170437 - 42*t^4 - 42*t^3 - 42*t^2 - 42*t + 1)
%t A170437 coxG[{44,903,-42}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Jul 09 2017 *)
%K A170437 nonn
%O A170437 0,2
%A A170437 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009