cp's OEIS Frontend

A170638 Number of reduced words of length n in Coxeter group on 5 generators S_i with relations (S_i)^2 = (S_i S_j)^49 = I.

%I A170638 #8 Nov 21 2016 11:11:15
%S A170638 1,5,20,80,320,1280,5120,20480,81920,327680,1310720,5242880,20971520,
%T A170638 83886080,335544320,1342177280,5368709120,21474836480,85899345920,
%U A170638 343597383680,1374389534720,5497558138880,21990232555520,87960930222080
%N A170638 Number of reduced words of length n in Coxeter group on 5 generators S_i with relations (S_i)^2 = (S_i S_j)^49 = I.
%C A170638 The initial terms coincide with those of A003947, although the two sequences are eventually different.
%C A170638 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170638 <a href="/index/Rec#order_49">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, 3, -6).
%F A170638 G.f. (t^49 + 2*t^48 + 2*t^47 + 2*t^46 + 2*t^45 + 2*t^44 + 2*t^43 + 2*t^42 +
%F A170638 2*t^41 + 2*t^40 + 2*t^39 + 2*t^38 + 2*t^37 + 2*t^36 + 2*t^35 + 2*t^34 +
%F A170638 2*t^33 + 2*t^32 + 2*t^31 + 2*t^30 + 2*t^29 + 2*t^28 + 2*t^27 + 2*t^26 +
%F A170638 2*t^25 + 2*t^24 + 2*t^23 + 2*t^22 + 2*t^21 + 2*t^20 + 2*t^19 + 2*t^18 +
%F A170638 2*t^17 + 2*t^16 + 2*t^15 + 2*t^14 + 2*t^13 + 2*t^12 + 2*t^11 + 2*t^10 +
%F A170638 2*t^9 + 2*t^8 + 2*t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t +
%F A170638 1)/(6*t^49 - 3*t^48 - 3*t^47 - 3*t^46 - 3*t^45 - 3*t^44 - 3*t^43 -
%F A170638 3*t^42 - 3*t^41 - 3*t^40 - 3*t^39 - 3*t^38 - 3*t^37 - 3*t^36 - 3*t^35 -
%F A170638 3*t^34 - 3*t^33 - 3*t^32 - 3*t^31 - 3*t^30 - 3*t^29 - 3*t^28 - 3*t^27 -
%F A170638 3*t^26 - 3*t^25 - 3*t^24 - 3*t^23 - 3*t^22 - 3*t^21 - 3*t^20 - 3*t^19 -
%F A170638 3*t^18 - 3*t^17 - 3*t^16 - 3*t^15 - 3*t^14 - 3*t^13 - 3*t^12 - 3*t^11 -
%F A170638 3*t^10 - 3*t^9 - 3*t^8 - 3*t^7 - 3*t^6 - 3*t^5 - 3*t^4 - 3*t^3 - 3*t^2 -
%F A170638 3*t + 1)
%t A170638 coxG[{49,6,-3,30}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Jun 28 2015 *)
%K A170638 nonn
%O A170638 0,2
%A A170638 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009