cp's OEIS Frontend

A169366 Number of reduced words of length n in Coxeter group on 17 generators S_i with relations (S_i)^2 = (S_i S_j)^31 = I.

%I A169366 #10 May 08 2018 00:29:25
%S A169366 1,17,272,4352,69632,1114112,17825792,285212672,4563402752,
%T A169366 73014444032,1168231104512,18691697672192,299067162755072,
%U A169366 4785074604081152,76561193665298432,1224979098644774912,19599665578316398592
%N A169366 Number of reduced words of length n in Coxeter group on 17 generators S_i with relations (S_i)^2 = (S_i S_j)^31 = I.
%C A169366 The initial terms coincide with those of A170736, although the two sequences are eventually different.
%C A169366 First disagreement at index 31: a(31) = 22596875928343569839364720024765857656, A170736(31) = 22596875928343569839364720024765857792. - _Klaus Brockhaus_, Jun 17 2011
%C A169366 Computed with Magma using commands similar to those used to compute A154638.
%H A169366 <a href="/index/Rec#order_31">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, -120).
%F A169366 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)/(120*t^31 - 15*t^30 - 15*t^29 - 15*t^28 - 15*t^27 - 15*t^26 - 15*t^25 - 15*t^24 - 15*t^23 - 15*t^22 - 15*t^21 - 15*t^20 - 15*t^19 - 15*t^18 - 15*t^17 - 15*t^16 - 15*t^15 - 15*t^14 - 15*t^13 - 15*t^12 - 15*t^11 - 15*t^10 - 15*t^9 - 15*t^8 - 15*t^7 - 15*t^6 - 15*t^5 - 15*t^4 - 15*t^3 - 15*t^2 - 15*t + 1).
%Y A169366 Cf. A170736 (G.f.: (1+x)/(1-16*x)).
%K A169366 nonn
%O A169366 0,2
%A A169366 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009