cp's OEIS Frontend

A170014 Number of reduced words of length n in Coxeter group on 5 generators S_i with relations (S_i)^2 = (S_i S_j)^36 = I.

%I A170014 #8 Jul 09 2024 17:18:46
%S A170014 1,5,20,80,320,1280,5120,20480,81920,327680,1310720,5242880,20971520,
%T A170014 83886080,335544320,1342177280,5368709120,21474836480,85899345920,
%U A170014 343597383680,1374389534720,5497558138880,21990232555520,87960930222080
%N A170014 Number of reduced words of length n in Coxeter group on 5 generators S_i with relations (S_i)^2 = (S_i S_j)^36 = I.
%C A170014 The initial terms coincide with those of A003947, although the two sequences are eventually different.
%C A170014 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170014 <a href="/index/Rec#order_36">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, -6).
%F A170014 G.f. (t^36 + 2*t^35 + 2*t^34 + 2*t^33 + 2*t^32 + 2*t^31 + 2*t^30 + 2*t^29 +
%F A170014 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 A170014 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 A170014 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 A170014 + 2*t^3 + 2*t^2 + 2*t + 1)/(6*t^36 - 3*t^35 - 3*t^34 - 3*t^33 - 3*t^32 -
%F A170014 3*t^31 - 3*t^30 - 3*t^29 - 3*t^28 - 3*t^27 - 3*t^26 - 3*t^25 - 3*t^24 -
%F A170014 3*t^23 - 3*t^22 - 3*t^21 - 3*t^20 - 3*t^19 - 3*t^18 - 3*t^17 - 3*t^16 -
%F A170014 3*t^15 - 3*t^14 - 3*t^13 - 3*t^12 - 3*t^11 - 3*t^10 - 3*t^9 - 3*t^8 -
%F A170014 3*t^7 - 3*t^6 - 3*t^5 - 3*t^4 - 3*t^3 - 3*t^2 - 3*t + 1)
%t A170014 coxG[{36,6,-3,30}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Jul 09 2024 *)
%K A170014 nonn
%O A170014 0,2
%A A170014 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009