cp's OEIS Frontend

A170042 Number of reduced words of length n in Coxeter group on 33 generators S_i with relations (S_i)^2 = (S_i S_j)^36 = I.

%I A170042 #8 Nov 26 2016 09:46:08
%S A170042 1,33,1056,33792,1081344,34603008,1107296256,35433480192,
%T A170042 1133871366144,36283883716608,1161084278931456,37154696925806592,
%U A170042 1188950301625810944,38046409652025950208,1217485108864830406656,38959523483674573012992
%N A170042 Number of reduced words of length n in Coxeter group on 33 generators S_i with relations (S_i)^2 = (S_i S_j)^36 = I.
%C A170042 The initial terms coincide with those of A170752, although the two sequences are eventually different.
%C A170042 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170042 <a href="/index/Rec#order_36">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, -496).
%F A170042 G.f. (t^36 + 2*t^35 + 2*t^34 + 2*t^33 + 2*t^32 + 2*t^31 + 2*t^30 + 2*t^29 +
%F A170042 2*t^28 + 2*t^27 + 2*t^26 + 2*t^25 + 2*t^24 + 2*t^23 + 2*t^22 + 2*t^21 +
%F A170042 2*t^20 + 2*t^19 + 2*t^18 + 2*t^17 + 2*t^16 + 2*t^15 + 2*t^14 + 2*t^13 +
%F A170042 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
%F A170042 + 2*t^3 + 2*t^2 + 2*t + 1)/(496*t^36 - 31*t^35 - 31*t^34 - 31*t^33 -
%F A170042 31*t^32 - 31*t^31 - 31*t^30 - 31*t^29 - 31*t^28 - 31*t^27 - 31*t^26 -
%F A170042 31*t^25 - 31*t^24 - 31*t^23 - 31*t^22 - 31*t^21 - 31*t^20 - 31*t^19 -
%F A170042 31*t^18 - 31*t^17 - 31*t^16 - 31*t^15 - 31*t^14 - 31*t^13 - 31*t^12 -
%F A170042 31*t^11 - 31*t^10 - 31*t^9 - 31*t^8 - 31*t^7 - 31*t^6 - 31*t^5 - 31*t^4
%F A170042 - 31*t^3 - 31*t^2 - 31*t + 1)
%t A170042 coxG[{36,496,-31}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Jun 02 2016 *)
%K A170042 nonn
%O A170042 0,2
%A A170042 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009