cp's OEIS Frontend

A169378 Number of reduced words of length n in Coxeter group on 29 generators S_i with relations (S_i)^2 = (S_i S_j)^31 = I.

%I A169378 #15 Oct 11 2024 06:58:23
%S A169378 1,29,812,22736,636608,17825024,499100672,13974818816,391294926848,
%T A169378 10956257951744,306775222648832,8589706234167296,240511774556684288,
%U A169378 6734329687587160064,188561231252440481792,5279714475068333490176
%N A169378 Number of reduced words of length n in Coxeter group on 29 generators S_i with relations (S_i)^2 = (S_i S_j)^31 = I.
%C A169378 The initial terms coincide with those of A170748, although the two sequences are eventually different.
%C A169378 First disagreement at index 31: a(31) = 753596613502928730875453549568497677758365290, A170748(31) = 753596613502928730875453549568497677758365696. - _Klaus Brockhaus_, Jun 17 2011
%C A169378 Computed with Magma using commands similar to those used to compute A154638.
%H A169378 <a href="/index/Rec#order_31">Index entries for linear recurrences with constant coefficients</a>, signature (27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, -378).
%F A169378 G.f.: (t^31 + 2*t^30 + 2*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)/(378*t^31 - 27*t^30 - 27*t^29 - 27*t^28 - 27*t^27 - 27*t^26 - 27*t^25 - 27*t^24 - 27*t^23 - 27*t^22 - 27*t^21 - 27*t^20 - 27*t^19 - 27*t^18 - 27*t^17 - 27*t^16 - 27*t^15 - 27*t^14 - 27*t^13 - 27*t^12 - 27*t^11 - 27*t^10 - 27*t^9 - 27*t^8 - 27*t^7 - 27*t^6 - 27*t^5 - 27*t^4 - 27*t^3 - 27*t^2 - 27*t + 1).
%t A169378 coxG[{31,378,-27}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Mar 17 2023 *)
%Y A169378 Cf. A170748 (G.f.: (1+x)/(1-28*x)).
%K A169378 nonn
%O A169378 0,2
%A A169378 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009