cp's OEIS Frontend

A170411 Number of reduced words of length n in Coxeter group on 18 generators S_i with relations (S_i)^2 = (S_i S_j)^44 = I.

%I A170411 #8 Jun 03 2020 15:53:24
%S A170411 1,18,306,5202,88434,1503378,25557426,434476242,7386096114,
%T A170411 125563633938,2134581776946,36287890208082,616894133537394,
%U A170411 10487200270135698,178282404592306866,3030800878069216722,51523614927176684274
%N A170411 Number of reduced words of length n in Coxeter group on 18 generators S_i with relations (S_i)^2 = (S_i S_j)^44 = I.
%C A170411 The initial terms coincide with those of A170737, although the two sequences are eventually different.
%C A170411 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170411 <a href="/index/Rec#order_44">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, -136).
%F A170411 G.f. (t^44 + 2*t^43 + 2*t^42 + 2*t^41 + 2*t^40 + 2*t^39 + 2*t^38 + 2*t^37 +
%F A170411 2*t^36 + 2*t^35 + 2*t^34 + 2*t^33 + 2*t^32 + 2*t^31 + 2*t^30 + 2*t^29 +
%F A170411 2*t^28 + 2*t^27 + 2*t^26 + 2*t^25 + 2*t^24 + 2*t^23 + 2*t^22 + 2*t^21 +
%F A170411 2*t^20 + 2*t^19 + 2*t^18 + 2*t^17 + 2*t^16 + 2*t^15 + 2*t^14 + 2*t^13 +
%F A170411 2*t^12 + 2*t^11 + 2*t^10 + 2*t^9 + 2*t^8 + 2*t^7 + 2*t^6 + 2*t^5 + 2*t^4
%F A170411 + 2*t^3 + 2*t^2 + 2*t + 1)/(136*t^44 - 16*t^43 - 16*t^42 - 16*t^41 -
%F A170411 16*t^40 - 16*t^39 - 16*t^38 - 16*t^37 - 16*t^36 - 16*t^35 - 16*t^34 -
%F A170411 16*t^33 - 16*t^32 - 16*t^31 - 16*t^30 - 16*t^29 - 16*t^28 - 16*t^27 -
%F A170411 16*t^26 - 16*t^25 - 16*t^24 - 16*t^23 - 16*t^22 - 16*t^21 - 16*t^20 -
%F A170411 16*t^19 - 16*t^18 - 16*t^17 - 16*t^16 - 16*t^15 - 16*t^14 - 16*t^13 -
%F A170411 16*t^12 - 16*t^11 - 16*t^10 - 16*t^9 - 16*t^8 - 16*t^7 - 16*t^6 - 16*t^5
%F A170411 - 16*t^4 - 16*t^3 - 16*t^2 - 16*t + 1)
%t A170411 coxG[{44,136,-16}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Jun 03 2020 *)
%K A170411 nonn
%O A170411 0,2
%A A170411 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009