cp's OEIS Frontend

A170586 Number of reduced words of length n in Coxeter group on 49 generators S_i with relations (S_i)^2 = (S_i S_j)^47 = I.

%I A170586 #10 Jun 21 2022 23:36:27
%S A170586 1,49,2352,112896,5419008,260112384,12485394432,599298932736,
%T A170586 28766348771328,1380784741023744,66277667569139712,
%U A170586 3181328043318706176,152703746079297896448,7329779811806299029504,351829430966702353416192
%N A170586 Number of reduced words of length n in Coxeter group on 49 generators S_i with relations (S_i)^2 = (S_i S_j)^47 = I.
%C A170586 The initial terms coincide with those of A170768, although the two sequences are eventually different.
%C A170586 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170586 <a href="/index/Rec#order_47">Index entries for linear recurrences with constant coefficients</a>, signature (47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, -1128).
%F A170586 G.f.: (t^47 + 2*t^46 + 2*t^45 + 2*t^44 + 2*t^43 + 2*t^42 + 2*t^41 + 2*t^40 +
%F A170586 2*t^39 + 2*t^38 + 2*t^37 + 2*t^36 + 2*t^35 + 2*t^34 + 2*t^33 + 2*t^32 +
%F A170586 2*t^31 + 2*t^30 + 2*t^29 + 2*t^28 + 2*t^27 + 2*t^26 + 2*t^25 + 2*t^24 +
%F A170586 2*t^23 + 2*t^22 + 2*t^21 + 2*t^20 + 2*t^19 + 2*t^18 + 2*t^17 + 2*t^16 +
%F A170586 2*t^15 + 2*t^14 + 2*t^13 + 2*t^12 + 2*t^11 + 2*t^10 + 2*t^9 + 2*t^8 +
%F A170586 2*t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(1128*t^47 -
%F A170586 47*t^46 - 47*t^45 - 47*t^44 - 47*t^43 - 47*t^42 - 47*t^41 - 47*t^40 -
%F A170586 47*t^39 - 47*t^38 - 47*t^37 - 47*t^36 - 47*t^35 - 47*t^34 - 47*t^33 -
%F A170586 47*t^32 - 47*t^31 - 47*t^30 - 47*t^29 - 47*t^28 - 47*t^27 - 47*t^26 -
%F A170586 47*t^25 - 47*t^24 - 47*t^23 - 47*t^22 - 47*t^21 - 47*t^20 - 47*t^19 -
%F A170586 47*t^18 - 47*t^17 - 47*t^16 - 47*t^15 - 47*t^14 - 47*t^13 - 47*t^12 -
%F A170586 47*t^11 - 47*t^10 - 47*t^9 - 47*t^8 - 47*t^7 - 47*t^6 - 47*t^5 - 47*t^4
%F A170586 - 47*t^3 - 47*t^2 - 47*t + 1).
%t A170586 coxG[{47,1128,-47}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Sep 13 2018 *)
%K A170586 nonn
%O A170586 0,2
%A A170586 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009