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A170651 Number of reduced words of length n in Coxeter group on 18 generators S_i with relations (S_i)^2 = (S_i S_j)^49 = I.

%I A170651 #8 Oct 01 2018 14:13:34
%S A170651 1,18,306,5202,88434,1503378,25557426,434476242,7386096114,
%T A170651 125563633938,2134581776946,36287890208082,616894133537394,
%U A170651 10487200270135698,178282404592306866,3030800878069216722,51523614927176684274
%N A170651 Number of reduced words of length n in Coxeter group on 18 generators S_i with relations (S_i)^2 = (S_i S_j)^49 = I.
%C A170651 The initial terms coincide with those of A170737, although the two sequences are eventually different.
%C A170651 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170651 <a href="/index/Rec#order_49">Index entries for linear recurrences with constant coefficients</a>, signature (16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, -136).
%F A170651 G.f. (t^49 + 2*t^48 + 2*t^47 + 2*t^46 + 2*t^45 + 2*t^44 + 2*t^43 + 2*t^42 +
%F A170651 2*t^41 + 2*t^40 + 2*t^39 + 2*t^38 + 2*t^37 + 2*t^36 + 2*t^35 + 2*t^34 +
%F A170651 2*t^33 + 2*t^32 + 2*t^31 + 2*t^30 + 2*t^29 + 2*t^28 + 2*t^27 + 2*t^26 +
%F A170651 2*t^25 + 2*t^24 + 2*t^23 + 2*t^22 + 2*t^21 + 2*t^20 + 2*t^19 + 2*t^18 +
%F A170651 2*t^17 + 2*t^16 + 2*t^15 + 2*t^14 + 2*t^13 + 2*t^12 + 2*t^11 + 2*t^10 +
%F A170651 2*t^9 + 2*t^8 + 2*t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t +
%F A170651 1)/(136*t^49 - 16*t^48 - 16*t^47 - 16*t^46 - 16*t^45 - 16*t^44 - 16*t^43
%F A170651 - 16*t^42 - 16*t^41 - 16*t^40 - 16*t^39 - 16*t^38 - 16*t^37 - 16*t^36 -
%F A170651 16*t^35 - 16*t^34 - 16*t^33 - 16*t^32 - 16*t^31 - 16*t^30 - 16*t^29 -
%F A170651 16*t^28 - 16*t^27 - 16*t^26 - 16*t^25 - 16*t^24 - 16*t^23 - 16*t^22 -
%F A170651 16*t^21 - 16*t^20 - 16*t^19 - 16*t^18 - 16*t^17 - 16*t^16 - 16*t^15 -
%F A170651 16*t^14 - 16*t^13 - 16*t^12 - 16*t^11 - 16*t^10 - 16*t^9 - 16*t^8 -
%F A170651 16*t^7 - 16*t^6 - 16*t^5 - 16*t^4 - 16*t^3 - 16*t^2 - 16*t + 1)
%t A170651 coxG[{49, 136, -16}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Oct 01 2018 *)
%K A170651 nonn
%O A170651 0,2
%A A170651 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009