cp's OEIS Frontend

A170269 Number of reduced words of length n in Coxeter group on 20 generators S_i with relations (S_i)^2 = (S_i S_j)^41 = I.

%I A170269 #8 Sep 05 2022 12:19:40
%S A170269 1,20,380,7220,137180,2606420,49521980,940917620,17877434780,
%T A170269 339671260820,6453753955580,122621325156020,2329805177964380,
%U A170269 44266298381323220,841059669245141180,15980133715657682420
%N A170269 Number of reduced words of length n in Coxeter group on 20 generators S_i with relations (S_i)^2 = (S_i S_j)^41 = I.
%C A170269 The initial terms coincide with those of A170739, although the two sequences are eventually different.
%C A170269 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170269 <a href="/index/Rec#order_41">Index entries for linear recurrences with constant coefficients</a>, signature (18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, -171).
%F A170269 G.f.: (t^41 + 2*t^40 + 2*t^39 + 2*t^38 + 2*t^37 + 2*t^36 + 2*t^35 + 2*t^34 +
%F A170269 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 A170269 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 A170269 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 A170269 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 A170269 1)/(171*t^41 - 18*t^40 - 18*t^39 - 18*t^38 - 18*t^37 - 18*t^36 - 18*t^35
%F A170269 - 18*t^34 - 18*t^33 - 18*t^32 - 18*t^31 - 18*t^30 - 18*t^29 - 18*t^28 -
%F A170269 18*t^27 - 18*t^26 - 18*t^25 - 18*t^24 - 18*t^23 - 18*t^22 - 18*t^21 -
%F A170269 18*t^20 - 18*t^19 - 18*t^18 - 18*t^17 - 18*t^16 - 18*t^15 - 18*t^14 -
%F A170269 18*t^13 - 18*t^12 - 18*t^11 - 18*t^10 - 18*t^9 - 18*t^8 - 18*t^7 -
%F A170269 18*t^6 - 18*t^5 - 18*t^4 - 18*t^3 - 18*t^2 - 18*t + 1).
%F A170269 a(n) = -171*a(n-41) + 18*Sum_{k=1..40} a(n-k). - _Wesley Ivan Hurt_, Sep 05 2022
%K A170269 nonn
%O A170269 0,2
%A A170269 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009