cp's OEIS Frontend

A170558 Number of reduced words of length n in Coxeter group on 21 generators S_i with relations (S_i)^2 = (S_i S_j)^47 = I.

%I A170558 #8 Nov 11 2020 14:51:50
%S A170558 1,21,420,8400,168000,3360000,67200000,1344000000,26880000000,
%T A170558 537600000000,10752000000000,215040000000000,4300800000000000,
%U A170558 86016000000000000,1720320000000000000,34406400000000000000
%N A170558 Number of reduced words of length n in Coxeter group on 21 generators S_i with relations (S_i)^2 = (S_i S_j)^47 = I.
%C A170558 The initial terms coincide with those of A170740, although the two sequences are eventually different.
%C A170558 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170558 <a href="/index/Rec#order_47">Index entries for linear recurrences with constant coefficients</a>, signature (19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, -190).
%F A170558 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 A170558 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 A170558 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 A170558 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 A170558 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 A170558 2*t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(190*t^47 -
%F A170558 19*t^46 - 19*t^45 - 19*t^44 - 19*t^43 - 19*t^42 - 19*t^41 - 19*t^40 -
%F A170558 19*t^39 - 19*t^38 - 19*t^37 - 19*t^36 - 19*t^35 - 19*t^34 - 19*t^33 -
%F A170558 19*t^32 - 19*t^31 - 19*t^30 - 19*t^29 - 19*t^28 - 19*t^27 - 19*t^26 -
%F A170558 19*t^25 - 19*t^24 - 19*t^23 - 19*t^22 - 19*t^21 - 19*t^20 - 19*t^19 -
%F A170558 19*t^18 - 19*t^17 - 19*t^16 - 19*t^15 - 19*t^14 - 19*t^13 - 19*t^12 -
%F A170558 19*t^11 - 19*t^10 - 19*t^9 - 19*t^8 - 19*t^7 - 19*t^6 - 19*t^5 - 19*t^4
%F A170558 - 19*t^3 - 19*t^2 - 19*t + 1)
%t A170558 coxG[{47,190,-19}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Nov 11 2020 *)
%K A170558 nonn
%O A170558 0,2
%A A170558 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009