cp's OEIS Frontend

A168790 Number of reduced words of length n in Coxeter group on 17 generators S_i with relations (S_i)^2 = (S_i S_j)^19 = I.

%I A168790 #12 Nov 24 2016 16:18:17
%S A168790 1,17,272,4352,69632,1114112,17825792,285212672,4563402752,
%T A168790 73014444032,1168231104512,18691697672192,299067162755072,
%U A168790 4785074604081152,76561193665298432,1224979098644774912,19599665578316398592
%N A168790 Number of reduced words of length n in Coxeter group on 17 generators S_i with relations (S_i)^2 = (S_i S_j)^19 = I.
%C A168790 The initial terms coincide with those of A170736, although the two sequences are eventually different.
%C A168790 First disagreement at index 19: a(19) = 80280230208783968632696, A170736(19) = 80280230208783968632832. - _Klaus Brockhaus_, Mar 30 2011
%C A168790 Computed with MAGMA using commands similar to those used to compute A154638.
%H A168790 G. C. Greubel, <a href="/A168790/b168790.txt">Table of n, a(n) for n = 0..500</a>
%H A168790 <a href="/index/Rec#order_19">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, -120).
%F A168790 G.f.: (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^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).
%t A168790 CoefficientList[Series[(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^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), {t, 0, 50}], t] (* _G. C. Greubel_, Aug 15 2016 *)
%Y A168790 Cf. A170736 (G.f.: (1+x)/(1-16*x)).
%K A168790 nonn
%O A168790 0,2
%A A168790 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009