cp's OEIS Frontend

A169289 Number of reduced words of length n in Coxeter group on 36 generators S_i with relations (S_i)^2 = (S_i S_j)^29 = I.

%I A169289 #12 Oct 16 2023 12:06:32
%S A169289 1,36,1260,44100,1543500,54022500,1890787500,66177562500,
%T A169289 2316214687500,81067514062500,2837362992187500,99307704726562500,
%U A169289 3475769665429687500,121651938290039062500,4257817840151367187500,149023624405297851562500
%N A169289 Number of reduced words of length n in Coxeter group on 36 generators S_i with relations (S_i)^2 = (S_i S_j)^29 = I.
%C A169289 The initial terms coincide with those of A170755, although the two sequences are eventually different.
%C A169289 First disagreement at index 29: a(29) = 616890017524757928966165930032730102539061870, A170755(29) = 616890017524757928966165930032730102539062500. - _Klaus Brockhaus_, Jun 03 2011
%C A169289 Computed with Magma using commands similar to those used to compute A154638.
%H A169289 <a href="/index/Rec#order_29">Index entries for linear recurrences with constant coefficients</a>, signature (34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, -595).
%F A169289 G.f.: (t^29 + 2*t^28 + 2*t^27 + 2*t^26 + 2*t^25 + 2*t^24 + 2*t^23 + 2*t^22 + 2*t^21 + 2*t^20 + 2*t^19 + 2*t^18 + 2*t^17 + 2*t^16 + 2*t^15 + 2*t^14 + 2*t^13 + 2*t^12 + 2*t^11 + 2*t^10 + 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 + 1)/(595*t^29 - 34*t^28 - 34*t^27 - 34*t^26 - 34*t^25 - 34*t^24 - 34*t^23 - 34*t^22 - 34*t^21 - 34*t^20 - 34*t^19 - 34*t^18 - 34*t^17 - 34*t^16 - 34*t^15 - 34*t^14 - 34*t^13 - 34*t^12 - 34*t^11 - 34*t^10 - 34*t^9 - 34*t^8 - 34*t^7 - 34*t^6 - 34*t^5 - 34*t^4 - 34*t^3 - 34*t^2 - 34*t + 1).
%t A169289 coxG[{29,595,-34}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Oct 16 2023 *)
%Y A169289 Cf. A170755 (G.f.: (1+x)/(1-35*x)).
%K A169289 nonn
%O A169289 0,2
%A A169289 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009