cp's OEIS Frontend

A169478 Number of reduced words of length n in Coxeter group on 33 generators S_i with relations (S_i)^2 = (S_i S_j)^33 = I.

%I A169478 #8 Dec 17 2021 19:27:39
%S A169478 1,33,1056,33792,1081344,34603008,1107296256,35433480192,
%T A169478 1133871366144,36283883716608,1161084278931456,37154696925806592,
%U A169478 1188950301625810944,38046409652025950208,1217485108864830406656,38959523483674573012992
%N A169478 Number of reduced words of length n in Coxeter group on 33 generators S_i with relations (S_i)^2 = (S_i S_j)^33 = I.
%C A169478 The initial terms coincide with those of A170752, although the two sequences are eventually different.
%C A169478 Computed with MAGMA using commands similar to those used to compute A154638.
%H A169478 <a href="/index/Rec#order_33">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, -496).
%F A169478 G.f. (t^33 + 2*t^32 + 2*t^31 + 2*t^30 + 2*t^29 + 2*t^28 + 2*t^27 + 2*t^26 +
%F A169478 2*t^25 + 2*t^24 + 2*t^23 + 2*t^22 + 2*t^21 + 2*t^20 + 2*t^19 + 2*t^18 +
%F A169478 2*t^17 + 2*t^16 + 2*t^15 + 2*t^14 + 2*t^13 + 2*t^12 + 2*t^11 + 2*t^10 +
%F A169478 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 +
%F A169478 1)/(496*t^33 - 31*t^32 - 31*t^31 - 31*t^30 - 31*t^29 - 31*t^28 - 31*t^27
%F A169478 - 31*t^26 - 31*t^25 - 31*t^24 - 31*t^23 - 31*t^22 - 31*t^21 - 31*t^20 -
%F A169478 31*t^19 - 31*t^18 - 31*t^17 - 31*t^16 - 31*t^15 - 31*t^14 - 31*t^13 -
%F A169478 31*t^12 - 31*t^11 - 31*t^10 - 31*t^9 - 31*t^8 - 31*t^7 - 31*t^6 - 31*t^5
%F A169478 - 31*t^4 - 31*t^3 - 31*t^2 - 31*t + 1)
%t A169478 coxG[{33,496,-31}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Dec 17 2021 *)
%K A169478 nonn
%O A169478 0,2
%A A169478 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009