cp's OEIS Frontend

A170302 Number of reduced words of length n in Coxeter group on 5 generators S_i with relations (S_i)^2 = (S_i S_j)^42 = I.

%I A170302 #8 Apr 18 2019 11:06:28
%S A170302 1,5,20,80,320,1280,5120,20480,81920,327680,1310720,5242880,20971520,
%T A170302 83886080,335544320,1342177280,5368709120,21474836480,85899345920,
%U A170302 343597383680,1374389534720,5497558138880,21990232555520,87960930222080
%N A170302 Number of reduced words of length n in Coxeter group on 5 generators S_i with relations (S_i)^2 = (S_i S_j)^42 = I.
%C A170302 The initial terms coincide with those of A003947, although the two sequences are eventually different.
%C A170302 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170302 <a href="/index/Rec#order_42">Index entries for linear recurrences with constant coefficients</a>, signature (3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, -6).
%F A170302 G.f. (t^42 + 2*t^41 + 2*t^40 + 2*t^39 + 2*t^38 + 2*t^37 + 2*t^36 + 2*t^35 +
%F A170302 2*t^34 + 2*t^33 + 2*t^32 + 2*t^31 + 2*t^30 + 2*t^29 + 2*t^28 + 2*t^27 +
%F A170302 2*t^26 + 2*t^25 + 2*t^24 + 2*t^23 + 2*t^22 + 2*t^21 + 2*t^20 + 2*t^19 +
%F A170302 2*t^18 + 2*t^17 + 2*t^16 + 2*t^15 + 2*t^14 + 2*t^13 + 2*t^12 + 2*t^11 +
%F A170302 2*t^10 + 2*t^9 + 2*t^8 + 2*t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 +
%F A170302 2*t + 1)/(6*t^42 - 3*t^41 - 3*t^40 - 3*t^39 - 3*t^38 - 3*t^37 - 3*t^36 -
%F A170302 3*t^35 - 3*t^34 - 3*t^33 - 3*t^32 - 3*t^31 - 3*t^30 - 3*t^29 - 3*t^28 -
%F A170302 3*t^27 - 3*t^26 - 3*t^25 - 3*t^24 - 3*t^23 - 3*t^22 - 3*t^21 - 3*t^20 -
%F A170302 3*t^19 - 3*t^18 - 3*t^17 - 3*t^16 - 3*t^15 - 3*t^14 - 3*t^13 - 3*t^12 -
%F A170302 3*t^11 - 3*t^10 - 3*t^9 - 3*t^8 - 3*t^7 - 3*t^6 - 3*t^5 - 3*t^4 - 3*t^3
%F A170302 - 3*t^2 - 3*t + 1)
%t A170302 coxG[{42,6,-3,30}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Apr 18 2019 *)
%K A170302 nonn
%O A170302 0,2
%A A170302 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009