cp's OEIS Frontend

A170578 Number of reduced words of length n in Coxeter group on 41 generators S_i with relations (S_i)^2 = (S_i S_j)^47 = I.

%I A170578 #6 Nov 21 2016 13:06:00
%S A170578 1,41,1640,65600,2624000,104960000,4198400000,167936000000,
%T A170578 6717440000000,268697600000000,10747904000000000,429916160000000000,
%U A170578 17196646400000000000,687865856000000000000,27514634240000000000000
%N A170578 Number of reduced words of length n in Coxeter group on 41 generators S_i with relations (S_i)^2 = (S_i S_j)^47 = I.
%C A170578 The initial terms coincide with those of A170760, although the two sequences are eventually different.
%C A170578 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170578 <a href="/index/Rec#order_47">Index entries for linear recurrences with constant coefficients</a>, signature (39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, -780).
%F A170578 G.f. (t^47 + 2*t^46 + 2*t^45 + 2*t^44 + 2*t^43 + 2*t^42 + 2*t^41 + 2*t^40 +
%F A170578 2*t^39 + 2*t^38 + 2*t^37 + 2*t^36 + 2*t^35 + 2*t^34 + 2*t^33 + 2*t^32 +
%F A170578 2*t^31 + 2*t^30 + 2*t^29 + 2*t^28 + 2*t^27 + 2*t^26 + 2*t^25 + 2*t^24 +
%F A170578 2*t^23 + 2*t^22 + 2*t^21 + 2*t^20 + 2*t^19 + 2*t^18 + 2*t^17 + 2*t^16 +
%F A170578 2*t^15 + 2*t^14 + 2*t^13 + 2*t^12 + 2*t^11 + 2*t^10 + 2*t^9 + 2*t^8 +
%F A170578 2*t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(780*t^47 -
%F A170578 39*t^46 - 39*t^45 - 39*t^44 - 39*t^43 - 39*t^42 - 39*t^41 - 39*t^40 -
%F A170578 39*t^39 - 39*t^38 - 39*t^37 - 39*t^36 - 39*t^35 - 39*t^34 - 39*t^33 -
%F A170578 39*t^32 - 39*t^31 - 39*t^30 - 39*t^29 - 39*t^28 - 39*t^27 - 39*t^26 -
%F A170578 39*t^25 - 39*t^24 - 39*t^23 - 39*t^22 - 39*t^21 - 39*t^20 - 39*t^19 -
%F A170578 39*t^18 - 39*t^17 - 39*t^16 - 39*t^15 - 39*t^14 - 39*t^13 - 39*t^12 -
%F A170578 39*t^11 - 39*t^10 - 39*t^9 - 39*t^8 - 39*t^7 - 39*t^6 - 39*t^5 - 39*t^4
%F A170578 - 39*t^3 - 39*t^2 - 39*t + 1)
%K A170578 nonn
%O A170578 0,2
%A A170578 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009