A170402 - OEIS

%I #17 Nov 23 2025 15:26:15

%S 1,9,72,576,4608,36864,294912,2359296,18874368,150994944,1207959552,

%T 9663676416,77309411328,618475290624,4947802324992,39582418599936,

%U 316659348799488,2533274790395904,20266198323167232,162129586585337856

%N Number of reduced words of length n in Coxeter group on 9 generators S_i with relations (S_i)^2 = (S_i S_j)^44 = I.

%C The initial terms coincide with those of A003951, although the two sequences are eventually different.

%C Computed with Magma using commands similar to those used to compute A154638.

%H <a href="/index/Rec#order_44">Index entries for linear recurrences with constant coefficients</a>, signature (7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,-28).

%F G.f.: (t^44 + 2*t^43 + 2*t^42 + 2*t^41 + 2*t^40 + 2*t^39 + 2*t^38 + 2*t^37 +

%F 2*t^36 + 2*t^35 + 2*t^34 + 2*t^33 + 2*t^32 + 2*t^31 + 2*t^30 + 2*t^29 +

%F 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 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 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 + 2*t^3 + 2*t^2 + 2*t + 1)/(28*t^44 - 7*t^43 - 7*t^42 - 7*t^41 - 7*t^40

%F - 7*t^39 - 7*t^38 - 7*t^37 - 7*t^36 - 7*t^35 - 7*t^34 - 7*t^33 - 7*t^32

%F - 7*t^31 - 7*t^30 - 7*t^29 - 7*t^28 - 7*t^27 - 7*t^26 - 7*t^25 - 7*t^24

%F - 7*t^23 - 7*t^22 - 7*t^21 - 7*t^20 - 7*t^19 - 7*t^18 - 7*t^17 - 7*t^16

%F - 7*t^15 - 7*t^14 - 7*t^13 - 7*t^12 - 7*t^11 - 7*t^10 - 7*t^9 - 7*t^8 -

%F 7*t^7 - 7*t^6 - 7*t^5 - 7*t^4 - 7*t^3 - 7*t^2 - 7*t + 1).

%t coxG[{44,28,-7}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Nov 21 2025 *)

%K nonn,easy

%O 0,2

%A _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009