cp's OEIS Frontend

A169414 Number of reduced words of length n in Coxeter group on 17 generators S_i with relations (S_i)^2 = (S_i S_j)^32 = I.

%I A169414 #14 Oct 12 2018 13:43:39
%S A169414 1,17,272,4352,69632,1114112,17825792,285212672,4563402752,
%T A169414 73014444032,1168231104512,18691697672192,299067162755072,
%U A169414 4785074604081152,76561193665298432,1224979098644774912,19599665578316398592
%N A169414 Number of reduced words of length n in Coxeter group on 17 generators S_i with relations (S_i)^2 = (S_i S_j)^32 = I.
%C A169414 The initial terms coincide with those of A170736, although the two sequences are eventually different.
%C A169414 First disagreement is at index 32, the difference is 136. - _Klaus Brockhaus_, Jun 27 2011
%C A169414 Computed with Magma using commands similar to those used to compute A154638.
%H A169414 <a href="/index/Rec#order_32">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, -120).
%F A169414 G.f.: (t^32 + 2*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^32 - 15*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).
%F A169414 G.f.: (1+2*sum(k=1..31, x^k)+x^32)/(1-15*sum(k=1..31, x^k)+120*x^32).
%t A169414 coxG[{32,120,-15}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Oct 12 2018 *)
%Y A169414 Cf. A170736 (G.f.: (1+x)/(1-16*x) ).
%K A169414 nonn
%O A169414 0,2
%A A169414 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009