cp's OEIS Frontend

A169382 Number of reduced words of length n in Coxeter group on 33 generators S_i with relations (S_i)^2 = (S_i S_j)^31 = I.

%I A169382 #14 Oct 11 2024 06:58:07
%S A169382 1,33,1056,33792,1081344,34603008,1107296256,35433480192,
%T A169382 1133871366144,36283883716608,1161084278931456,37154696925806592,
%U A169382 1188950301625810944,38046409652025950208,1217485108864830406656,38959523483674573012992
%N A169382 Number of reduced words of length n in Coxeter group on 33 generators S_i with relations (S_i)^2 = (S_i S_j)^31 = I.
%C A169382 The initial terms coincide with those of A170752, although the two sequences are eventually different.
%C A169382 First disagreement at index 31: a(31) = 47099173859296676074923436991833339500630638064, A170752(31) = 47099173859296676074923436991833339500630638592. - _Klaus Brockhaus_, Jun 17 2011
%C A169382 Computed with Magma using commands similar to those used to compute A154638.
%H A169382 <a href="/index/Rec#order_31">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, -496).
%F A169382 G.f.: (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)/(496*t^31 - 31*t^30 - 31*t^29 - 31*t^28 - 31*t^27 - 31*t^26 - 31*t^25 - 31*t^24 - 31*t^23 - 31*t^22 - 31*t^21 - 31*t^20 - 31*t^19 - 31*t^18 - 31*t^17 - 31*t^16 - 31*t^15 - 31*t^14 - 31*t^13 - 31*t^12 - 31*t^11 - 31*t^10 - 31*t^9 - 31*t^8 - 31*t^7 - 31*t^6 - 31*t^5 - 31*t^4 - 31*t^3 - 31*t^2 - 31*t + 1).
%Y A169382 Cf. A170752 (G.f.: (1+x)/(1-32*x)).
%K A169382 nonn
%O A169382 0,2
%A A169382 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009