cp's OEIS Frontend

A170603 Number of reduced words of length n in Coxeter group on 18 generators S_i with relations (S_i)^2 = (S_i S_j)^48 = I.

%I A170603 #8 Jul 30 2019 19:08:43
%S A170603 1,18,306,5202,88434,1503378,25557426,434476242,7386096114,
%T A170603 125563633938,2134581776946,36287890208082,616894133537394,
%U A170603 10487200270135698,178282404592306866,3030800878069216722,51523614927176684274
%N A170603 Number of reduced words of length n in Coxeter group on 18 generators S_i with relations (S_i)^2 = (S_i S_j)^48 = I.
%C A170603 The initial terms coincide with those of A170737, although the two sequences are eventually different.
%C A170603 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170603 <a href="/index/Rec#order_48">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, -136).
%F A170603 G.f. (t^48 + 2*t^47 + 2*t^46 + 2*t^45 + 2*t^44 + 2*t^43 + 2*t^42 + 2*t^41 +
%F A170603 2*t^40 + 2*t^39 + 2*t^38 + 2*t^37 + 2*t^36 + 2*t^35 + 2*t^34 + 2*t^33 +
%F A170603 2*t^32 + 2*t^31 + 2*t^30 + 2*t^29 + 2*t^28 + 2*t^27 + 2*t^26 + 2*t^25 +
%F A170603 2*t^24 + 2*t^23 + 2*t^22 + 2*t^21 + 2*t^20 + 2*t^19 + 2*t^18 + 2*t^17 +
%F A170603 2*t^16 + 2*t^15 + 2*t^14 + 2*t^13 + 2*t^12 + 2*t^11 + 2*t^10 + 2*t^9 +
%F A170603 2*t^8 + 2*t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t +
%F A170603 1)/(136*t^48 - 16*t^47 - 16*t^46 - 16*t^45 - 16*t^44 - 16*t^43 - 16*t^42
%F A170603 - 16*t^41 - 16*t^40 - 16*t^39 - 16*t^38 - 16*t^37 - 16*t^36 - 16*t^35 -
%F A170603 16*t^34 - 16*t^33 - 16*t^32 - 16*t^31 - 16*t^30 - 16*t^29 - 16*t^28 -
%F A170603 16*t^27 - 16*t^26 - 16*t^25 - 16*t^24 - 16*t^23 - 16*t^22 - 16*t^21 -
%F A170603 16*t^20 - 16*t^19 - 16*t^18 - 16*t^17 - 16*t^16 - 16*t^15 - 16*t^14 -
%F A170603 16*t^13 - 16*t^12 - 16*t^11 - 16*t^10 - 16*t^9 - 16*t^8 - 16*t^7 -
%F A170603 16*t^6 - 16*t^5 - 16*t^4 - 16*t^3 - 16*t^2 - 16*t + 1)
%t A170603 coxG[{48,136,-16}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Jul 30 2019 *)
%K A170603 nonn
%O A170603 0,2
%A A170603 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009