cp's OEIS Frontend

A169413 Number of reduced words of length n in Coxeter group on 16 generators S_i with relations (S_i)^2 = (S_i S_j)^32 = I.

%I A169413 #14 May 08 2018 00:55:38
%S A169413 1,16,240,3600,54000,810000,12150000,182250000,2733750000,41006250000,
%T A169413 615093750000,9226406250000,138396093750000,2075941406250000,
%U A169413 31139121093750000,467086816406250000,7006302246093750000
%N A169413 Number of reduced words of length n in Coxeter group on 16 generators S_i with relations (S_i)^2 = (S_i S_j)^32 = I.
%C A169413 The initial terms coincide with those of A170735, although the two sequences are eventually different.
%C A169413 First disagreement is at index 32, the difference is 105. - _Klaus Brockhaus_, Jun 27 2011
%C A169413 Computed with Magma using commands similar to those used to compute A154638.
%H A169413 <a href="/index/Rec#order_32">Index entries for linear recurrences with constant coefficients</a>, signature (14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, -105).
%F A169413 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)/(105*t^32 - 14*t^31 - 14*t^30 - 14*t^29 - 14*t^28 - 14*t^27 - 14*t^26 - 14*t^25 - 14*t^24 - 14*t^23 - 14*t^22 - 14*t^21 - 14*t^20 - 14*t^19 - 14*t^18 - 14*t^17 - 14*t^16 - 14*t^15 - 14*t^14 - 14*t^13 - 14*t^12 - 14*t^11 - 14*t^10 - 14*t^9 - 14*t^8 - 14*t^7 - 14*t^6 - 14*t^5 - 14*t^4 - 14*t^3 - 14*t^2 - 14*t + 1).
%F A169413 G.f.: (1+2*sum(k=1..31, x^k)+x^32)/(1-14*sum(k=1..31, x^k)+105*x^32).
%t A169413 coxG[{32,105,-14}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Aug 11 2015 *)
%Y A169413 Cf. A170735 (G.f.: (1+x)/(1-15*x) ).
%K A169413 nonn
%O A169413 0,2
%A A169413 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009