cp's OEIS Frontend

A170657 Number of reduced words of length n in Coxeter group on 24 generators S_i with relations (S_i)^2 = (S_i S_j)^49 = I.

%I A170657 #8 Jun 02 2023 15:06:31
%S A170657 1,24,552,12696,292008,6716184,154472232,3552861336,81715810728,
%T A170657 1879463646744,43227663875112,994236269127576,22867434189934248,
%U A170657 525950986368487704,12096872686475217192,278228071788929995416
%N A170657 Number of reduced words of length n in Coxeter group on 24 generators S_i with relations (S_i)^2 = (S_i S_j)^49 = I.
%C A170657 The initial terms coincide with those of A170743, although the two sequences are eventually different.
%C A170657 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170657 <a href="/index/Rec#order_49">Index entries for linear recurrences with constant coefficients</a>, signature (22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, -253).
%F A170657 G.f. (t^49 + 2*t^48 + 2*t^47 + 2*t^46 + 2*t^45 + 2*t^44 + 2*t^43 + 2*t^42 +
%F A170657 2*t^41 + 2*t^40 + 2*t^39 + 2*t^38 + 2*t^37 + 2*t^36 + 2*t^35 + 2*t^34 +
%F A170657 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 A170657 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 A170657 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 A170657 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 A170657 1)/(253*t^49 - 22*t^48 - 22*t^47 - 22*t^46 - 22*t^45 - 22*t^44 - 22*t^43
%F A170657 - 22*t^42 - 22*t^41 - 22*t^40 - 22*t^39 - 22*t^38 - 22*t^37 - 22*t^36 -
%F A170657 22*t^35 - 22*t^34 - 22*t^33 - 22*t^32 - 22*t^31 - 22*t^30 - 22*t^29 -
%F A170657 22*t^28 - 22*t^27 - 22*t^26 - 22*t^25 - 22*t^24 - 22*t^23 - 22*t^22 -
%F A170657 22*t^21 - 22*t^20 - 22*t^19 - 22*t^18 - 22*t^17 - 22*t^16 - 22*t^15 -
%F A170657 22*t^14 - 22*t^13 - 22*t^12 - 22*t^11 - 22*t^10 - 22*t^9 - 22*t^8 -
%F A170657 22*t^7 - 22*t^6 - 22*t^5 - 22*t^4 - 22*t^3 - 22*t^2 - 22*t + 1)
%t A170657 coxG[{49,253,-22}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Jun 02 2023 *)
%K A170657 nonn
%O A170657 0,2
%A A170657 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009