cp's OEIS Frontend

A170378 Number of reduced words of length n in Coxeter group on 33 generators S_i with relations (S_i)^2 = (S_i S_j)^43 = I.

%I A170378 #12 Nov 21 2016 19:29:52
%S A170378 1,33,1056,33792,1081344,34603008,1107296256,35433480192,
%T A170378 1133871366144,36283883716608,1161084278931456,37154696925806592,
%U A170378 1188950301625810944,38046409652025950208,1217485108864830406656,38959523483674573012992
%N A170378 Number of reduced words of length n in Coxeter group on 33 generators S_i with relations (S_i)^2 = (S_i S_j)^43 = I.
%C A170378 The initial terms coincide with those of A170752, although the two sequences are eventually different.
%C A170378 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170378 <a href="/index/Rec#order_43">Index entries for linear recurrences with constant coefficients</a>, signature (31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, -496).
%F A170378 G.f. (t^43 + 2*t^42 + 2*t^41 + 2*t^40 + 2*t^39 + 2*t^38 + 2*t^37 + 2*t^36 +
%F A170378 2*t^35 + 2*t^34 + 2*t^33 + 2*t^32 + 2*t^31 + 2*t^30 + 2*t^29 + 2*t^28 +
%F A170378 2*t^27 + 2*t^26 + 2*t^25 + 2*t^24 + 2*t^23 + 2*t^22 + 2*t^21 + 2*t^20 +
%F A170378 2*t^19 + 2*t^18 + 2*t^17 + 2*t^16 + 2*t^15 + 2*t^14 + 2*t^13 + 2*t^12 +
%F A170378 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
%F A170378 + 2*t^2 + 2*t + 1)/(496*t^43 - 31*t^42 - 31*t^41 - 31*t^40 - 31*t^39 -
%F A170378 31*t^38 - 31*t^37 - 31*t^36 - 31*t^35 - 31*t^34 - 31*t^33 - 31*t^32 -
%F A170378 31*t^31 - 31*t^30 - 31*t^29 - 31*t^28 - 31*t^27 - 31*t^26 - 31*t^25 -
%F A170378 31*t^24 - 31*t^23 - 31*t^22 - 31*t^21 - 31*t^20 - 31*t^19 - 31*t^18 -
%F A170378 31*t^17 - 31*t^16 - 31*t^15 - 31*t^14 - 31*t^13 - 31*t^12 - 31*t^11 -
%F A170378 31*t^10 - 31*t^9 - 31*t^8 - 31*t^7 - 31*t^6 - 31*t^5 - 31*t^4 - 31*t^3 -
%F A170378 31*t^2 - 31*t + 1)
%t A170378 With[{num=Total[2t^Range[42]]+t^43+1,den=Total[-31 t^Range[42]]+ 496t^43+ 1}, CoefficientList[Series[num/den,{t,0,20}],t]] (* _Harvey P. Dale_, Jun 18 2011 *)
%K A170378 nonn
%O A170378 0,2
%A A170378 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009