cp's OEIS Frontend

A170325 Number of reduced words of length n in Coxeter group on 28 generators S_i with relations (S_i)^2 = (S_i S_j)^42 = I.

%I A170325 #8 Oct 23 2018 15:13:18
%S A170325 1,28,756,20412,551124,14880348,401769396,10847773692,292889889684,
%T A170325 7908027021468,213516729579636,5764951698650172,155653695863554644,
%U A170325 4202649788315975388,113471544284531335476,3063731695682346057852
%N A170325 Number of reduced words of length n in Coxeter group on 28 generators S_i with relations (S_i)^2 = (S_i S_j)^42 = I.
%C A170325 The initial terms coincide with those of A170747, although the two sequences are eventually different.
%C A170325 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170325 <a href="/index/Rec#order_42">Index entries for linear recurrences with constant coefficients</a>, signature (26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, -351).
%F A170325 G.f. (t^42 + 2*t^41 + 2*t^40 + 2*t^39 + 2*t^38 + 2*t^37 + 2*t^36 + 2*t^35 +
%F A170325 2*t^34 + 2*t^33 + 2*t^32 + 2*t^31 + 2*t^30 + 2*t^29 + 2*t^28 + 2*t^27 +
%F A170325 2*t^26 + 2*t^25 + 2*t^24 + 2*t^23 + 2*t^22 + 2*t^21 + 2*t^20 + 2*t^19 +
%F A170325 2*t^18 + 2*t^17 + 2*t^16 + 2*t^15 + 2*t^14 + 2*t^13 + 2*t^12 + 2*t^11 +
%F A170325 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 +
%F A170325 2*t + 1)/(351*t^42 - 26*t^41 - 26*t^40 - 26*t^39 - 26*t^38 - 26*t^37 -
%F A170325 26*t^36 - 26*t^35 - 26*t^34 - 26*t^33 - 26*t^32 - 26*t^31 - 26*t^30 -
%F A170325 26*t^29 - 26*t^28 - 26*t^27 - 26*t^26 - 26*t^25 - 26*t^24 - 26*t^23 -
%F A170325 26*t^22 - 26*t^21 - 26*t^20 - 26*t^19 - 26*t^18 - 26*t^17 - 26*t^16 -
%F A170325 26*t^15 - 26*t^14 - 26*t^13 - 26*t^12 - 26*t^11 - 26*t^10 - 26*t^9 -
%F A170325 26*t^8 - 26*t^7 - 26*t^6 - 26*t^5 - 26*t^4 - 26*t^3 - 26*t^2 - 26*t + 1)
%t A170325 coxG[{42,351,-26}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Oct 23 2018 *)
%K A170325 nonn
%O A170325 0,2
%A A170325 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009