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A170510 Number of reduced words of length n in Coxeter group on 21 generators S_i with relations (S_i)^2 = (S_i S_j)^46 = I.

%I A170510 #8 Apr 08 2019 11:28:18
%S A170510 1,21,420,8400,168000,3360000,67200000,1344000000,26880000000,
%T A170510 537600000000,10752000000000,215040000000000,4300800000000000,
%U A170510 86016000000000000,1720320000000000000,34406400000000000000
%N A170510 Number of reduced words of length n in Coxeter group on 21 generators S_i with relations (S_i)^2 = (S_i S_j)^46 = I.
%C A170510 The initial terms coincide with those of A170740, although the two sequences are eventually different.
%C A170510 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170510 <a href="/index/Rec#order_46">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, -190).
%F A170510 G.f. (t^46 + 2*t^45 + 2*t^44 + 2*t^43 + 2*t^42 + 2*t^41 + 2*t^40 + 2*t^39 +
%F A170510 2*t^38 + 2*t^37 + 2*t^36 + 2*t^35 + 2*t^34 + 2*t^33 + 2*t^32 + 2*t^31 +
%F A170510 2*t^30 + 2*t^29 + 2*t^28 + 2*t^27 + 2*t^26 + 2*t^25 + 2*t^24 + 2*t^23 +
%F A170510 2*t^22 + 2*t^21 + 2*t^20 + 2*t^19 + 2*t^18 + 2*t^17 + 2*t^16 + 2*t^15 +
%F A170510 2*t^14 + 2*t^13 + 2*t^12 + 2*t^11 + 2*t^10 + 2*t^9 + 2*t^8 + 2*t^7 +
%F A170510 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(190*t^46 - 19*t^45 -
%F A170510 19*t^44 - 19*t^43 - 19*t^42 - 19*t^41 - 19*t^40 - 19*t^39 - 19*t^38 -
%F A170510 19*t^37 - 19*t^36 - 19*t^35 - 19*t^34 - 19*t^33 - 19*t^32 - 19*t^31 -
%F A170510 19*t^30 - 19*t^29 - 19*t^28 - 19*t^27 - 19*t^26 - 19*t^25 - 19*t^24 -
%F A170510 19*t^23 - 19*t^22 - 19*t^21 - 19*t^20 - 19*t^19 - 19*t^18 - 19*t^17 -
%F A170510 19*t^16 - 19*t^15 - 19*t^14 - 19*t^13 - 19*t^12 - 19*t^11 - 19*t^10 -
%F A170510 19*t^9 - 19*t^8 - 19*t^7 - 19*t^6 - 19*t^5 - 19*t^4 - 19*t^3 - 19*t^2 -
%F A170510 19*t + 1)
%t A170510 coxG[{46,190,-19}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Apr 08 2019 *)
%K A170510 nonn
%O A170510 0,2
%A A170510 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009