cp's OEIS Frontend

A170642 Number of reduced words of length n in Coxeter group on 9 generators S_i with relations (S_i)^2 = (S_i S_j)^49 = I.

%I A170642 #8 Jul 21 2021 12:11:29
%S A170642 1,9,72,576,4608,36864,294912,2359296,18874368,150994944,1207959552,
%T A170642 9663676416,77309411328,618475290624,4947802324992,39582418599936,
%U A170642 316659348799488,2533274790395904,20266198323167232,162129586585337856
%N A170642 Number of reduced words of length n in Coxeter group on 9 generators S_i with relations (S_i)^2 = (S_i S_j)^49 = I.
%C A170642 The initial terms coincide with those of A003951, although the two sequences are eventually different.
%C A170642 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170642 <a href="/index/Rec#order_49">Index entries for linear recurrences with constant coefficients</a>, signature (7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, -28).
%F A170642 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 A170642 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 A170642 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 A170642 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 A170642 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 A170642 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 A170642 1)/(28*t^49 - 7*t^48 - 7*t^47 - 7*t^46 - 7*t^45 - 7*t^44 - 7*t^43 -
%F A170642 7*t^42 - 7*t^41 - 7*t^40 - 7*t^39 - 7*t^38 - 7*t^37 - 7*t^36 - 7*t^35 -
%F A170642 7*t^34 - 7*t^33 - 7*t^32 - 7*t^31 - 7*t^30 - 7*t^29 - 7*t^28 - 7*t^27 -
%F A170642 7*t^26 - 7*t^25 - 7*t^24 - 7*t^23 - 7*t^22 - 7*t^21 - 7*t^20 - 7*t^19 -
%F A170642 7*t^18 - 7*t^17 - 7*t^16 - 7*t^15 - 7*t^14 - 7*t^13 - 7*t^12 - 7*t^11 -
%F A170642 7*t^10 - 7*t^9 - 7*t^8 - 7*t^7 - 7*t^6 - 7*t^5 - 7*t^4 - 7*t^3 - 7*t^2 -
%F A170642 7*t + 1)
%t A170642 coxG[{49,28,-7}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Jul 21 2021 *)
%K A170642 nonn
%O A170642 0,2
%A A170642 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009