cp's OEIS Frontend

A170590 Number of reduced words of length n in Coxeter group on 5 generators S_i with relations (S_i)^2 = (S_i S_j)^48 = I.

%I A170590 #8 Jun 26 2019 19:32:54
%S A170590 1,5,20,80,320,1280,5120,20480,81920,327680,1310720,5242880,20971520,
%T A170590 83886080,335544320,1342177280,5368709120,21474836480,85899345920,
%U A170590 343597383680,1374389534720,5497558138880,21990232555520,87960930222080
%N A170590 Number of reduced words of length n in Coxeter group on 5 generators S_i with relations (S_i)^2 = (S_i S_j)^48 = I.
%C A170590 The initial terms coincide with those of A003947, although the two sequences are eventually different.
%C A170590 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170590 <a href="/index/Rec#order_48">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, 3, 3, 3, 3, 3, 3, -6).
%F A170590 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 A170590 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 A170590 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 A170590 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 A170590 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 A170590 2*t^8 + 2*t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(6*t^48
%F A170590 - 3*t^47 - 3*t^46 - 3*t^45 - 3*t^44 - 3*t^43 - 3*t^42 - 3*t^41 - 3*t^40
%F A170590 - 3*t^39 - 3*t^38 - 3*t^37 - 3*t^36 - 3*t^35 - 3*t^34 - 3*t^33 - 3*t^32
%F A170590 - 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 A170590 - 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 A170590 - 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 A170590 3*t^7 - 3*t^6 - 3*t^5 - 3*t^4 - 3*t^3 - 3*t^2 - 3*t + 1)
%t A170590 coxG[{48,6,-3,30}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Jun 26 2019 *)
%K A170590 nonn
%O A170590 0,2
%A A170590 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009