cp's OEIS Frontend

A170410 Number of reduced words of length n in Coxeter group on 17 generators S_i with relations (S_i)^2 = (S_i S_j)^44 = I.

%I A170410 #8 Sep 07 2017 17:44:02
%S A170410 1,17,272,4352,69632,1114112,17825792,285212672,4563402752,
%T A170410 73014444032,1168231104512,18691697672192,299067162755072,
%U A170410 4785074604081152,76561193665298432,1224979098644774912,19599665578316398592
%N A170410 Number of reduced words of length n in Coxeter group on 17 generators S_i with relations (S_i)^2 = (S_i S_j)^44 = I.
%C A170410 The initial terms coincide with those of A170736, although the two sequences are eventually different.
%C A170410 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170410 <a href="/index/Rec#order_44">Index entries for linear recurrences with constant coefficients</a>, signature (15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, -120).
%F A170410 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 A170410 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 A170410 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 A170410 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 A170410 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 A170410 + 2*t^3 + 2*t^2 + 2*t + 1)/(120*t^44 - 15*t^43 - 15*t^42 - 15*t^41 -
%F A170410 15*t^40 - 15*t^39 - 15*t^38 - 15*t^37 - 15*t^36 - 15*t^35 - 15*t^34 -
%F A170410 15*t^33 - 15*t^32 - 15*t^31 - 15*t^30 - 15*t^29 - 15*t^28 - 15*t^27 -
%F A170410 15*t^26 - 15*t^25 - 15*t^24 - 15*t^23 - 15*t^22 - 15*t^21 - 15*t^20 -
%F A170410 15*t^19 - 15*t^18 - 15*t^17 - 15*t^16 - 15*t^15 - 15*t^14 - 15*t^13 -
%F A170410 15*t^12 - 15*t^11 - 15*t^10 - 15*t^9 - 15*t^8 - 15*t^7 - 15*t^6 - 15*t^5
%F A170410 - 15*t^4 - 15*t^3 - 15*t^2 - 15*t + 1)
%t A170410 coxG[{44,120,-15}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Sep 07 2017 *)
%K A170410 nonn
%O A170410 0,2
%A A170410 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009