cp's OEIS Frontend

A170051 Number of reduced words of length n in Coxeter group on 42 generators S_i with relations (S_i)^2 = (S_i S_j)^36 = I.

%I A170051 #8 Dec 07 2024 15:47:27
%S A170051 1,42,1722,70602,2894682,118681962,4865960442,199504378122,
%T A170051 8179679503002,335366859623082,13750041244546362,563751691026400842,
%U A170051 23113819332082434522,947666592615379815402,38854330297230572431482
%N A170051 Number of reduced words of length n in Coxeter group on 42 generators S_i with relations (S_i)^2 = (S_i S_j)^36 = I.
%C A170051 The initial terms coincide with those of A170761, although the two sequences are eventually different.
%C A170051 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170051 <a href="/index/Rec#order_36">Index entries for linear recurrences with constant coefficients</a>, signature (40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, -820).
%F A170051 G.f. (t^36 + 2*t^35 + 2*t^34 + 2*t^33 + 2*t^32 + 2*t^31 + 2*t^30 + 2*t^29 +
%F A170051 2*t^28 + 2*t^27 + 2*t^26 + 2*t^25 + 2*t^24 + 2*t^23 + 2*t^22 + 2*t^21 +
%F A170051 2*t^20 + 2*t^19 + 2*t^18 + 2*t^17 + 2*t^16 + 2*t^15 + 2*t^14 + 2*t^13 +
%F A170051 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
%F A170051 + 2*t^3 + 2*t^2 + 2*t + 1)/(820*t^36 - 40*t^35 - 40*t^34 - 40*t^33 -
%F A170051 40*t^32 - 40*t^31 - 40*t^30 - 40*t^29 - 40*t^28 - 40*t^27 - 40*t^26 -
%F A170051 40*t^25 - 40*t^24 - 40*t^23 - 40*t^22 - 40*t^21 - 40*t^20 - 40*t^19 -
%F A170051 40*t^18 - 40*t^17 - 40*t^16 - 40*t^15 - 40*t^14 - 40*t^13 - 40*t^12 -
%F A170051 40*t^11 - 40*t^10 - 40*t^9 - 40*t^8 - 40*t^7 - 40*t^6 - 40*t^5 - 40*t^4
%F A170051 - 40*t^3 - 40*t^2 - 40*t + 1)
%t A170051 coxG[{36,820,-40}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Dec 07 2024 *)
%K A170051 nonn
%O A170051 0,2
%A A170051 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009