cp's OEIS Frontend

A170333 Number of reduced words of length n in Coxeter group on 36 generators S_i with relations (S_i)^2 = (S_i S_j)^42 = I.

%I A170333 #8 Nov 25 2023 13:30:18
%S A170333 1,36,1260,44100,1543500,54022500,1890787500,66177562500,
%T A170333 2316214687500,81067514062500,2837362992187500,99307704726562500,
%U A170333 3475769665429687500,121651938290039062500,4257817840151367187500,149023624405297851562500
%N A170333 Number of reduced words of length n in Coxeter group on 36 generators S_i with relations (S_i)^2 = (S_i S_j)^42 = I.
%C A170333 The initial terms coincide with those of A170755, although the two sequences are eventually different.
%C A170333 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170333 <a href="/index/Rec#order_42">Index entries for linear recurrences with constant coefficients</a>, signature (34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, -595).
%F A170333 G.f. (t^42 + 2*t^41 + 2*t^40 + 2*t^39 + 2*t^38 + 2*t^37 + 2*t^36 + 2*t^35 +
%F A170333 2*t^34 + 2*t^33 + 2*t^32 + 2*t^31 + 2*t^30 + 2*t^29 + 2*t^28 + 2*t^27 +
%F A170333 2*t^26 + 2*t^25 + 2*t^24 + 2*t^23 + 2*t^22 + 2*t^21 + 2*t^20 + 2*t^19 +
%F A170333 2*t^18 + 2*t^17 + 2*t^16 + 2*t^15 + 2*t^14 + 2*t^13 + 2*t^12 + 2*t^11 +
%F A170333 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 +
%F A170333 2*t + 1)/(595*t^42 - 34*t^41 - 34*t^40 - 34*t^39 - 34*t^38 - 34*t^37 -
%F A170333 34*t^36 - 34*t^35 - 34*t^34 - 34*t^33 - 34*t^32 - 34*t^31 - 34*t^30 -
%F A170333 34*t^29 - 34*t^28 - 34*t^27 - 34*t^26 - 34*t^25 - 34*t^24 - 34*t^23 -
%F A170333 34*t^22 - 34*t^21 - 34*t^20 - 34*t^19 - 34*t^18 - 34*t^17 - 34*t^16 -
%F A170333 34*t^15 - 34*t^14 - 34*t^13 - 34*t^12 - 34*t^11 - 34*t^10 - 34*t^9 -
%F A170333 34*t^8 - 34*t^7 - 34*t^6 - 34*t^5 - 34*t^4 - 34*t^3 - 34*t^2 - 34*t + 1)
%t A170333 coxG[{42,595,-34}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Nov 25 2023 *)
%K A170333 nonn
%O A170333 0,2
%A A170333 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009