cp's OEIS Frontend

A170234 Number of reduced words of length n in Coxeter group on 33 generators S_i with relations (S_i)^2 = (S_i S_j)^40 = I.

%I A170234 #8 May 15 2025 19:04:09
%S A170234 1,33,1056,33792,1081344,34603008,1107296256,35433480192,
%T A170234 1133871366144,36283883716608,1161084278931456,37154696925806592,
%U A170234 1188950301625810944,38046409652025950208,1217485108864830406656,38959523483674573012992
%N A170234 Number of reduced words of length n in Coxeter group on 33 generators S_i with relations (S_i)^2 = (S_i S_j)^40 = I.
%C A170234 The initial terms coincide with those of A170752, although the two sequences are eventually different.
%C A170234 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170234 <a href="/index/Rec#order_40">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, -496).
%F A170234 G.f. (t^40 + 2*t^39 + 2*t^38 + 2*t^37 + 2*t^36 + 2*t^35 + 2*t^34 + 2*t^33 +
%F A170234 2*t^32 + 2*t^31 + 2*t^30 + 2*t^29 + 2*t^28 + 2*t^27 + 2*t^26 + 2*t^25 +
%F A170234 2*t^24 + 2*t^23 + 2*t^22 + 2*t^21 + 2*t^20 + 2*t^19 + 2*t^18 + 2*t^17 +
%F A170234 2*t^16 + 2*t^15 + 2*t^14 + 2*t^13 + 2*t^12 + 2*t^11 + 2*t^10 + 2*t^9 +
%F A170234 2*t^8 + 2*t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t +
%F A170234 1)/(496*t^40 - 31*t^39 - 31*t^38 - 31*t^37 - 31*t^36 - 31*t^35 - 31*t^34
%F A170234 - 31*t^33 - 31*t^32 - 31*t^31 - 31*t^30 - 31*t^29 - 31*t^28 - 31*t^27 -
%F A170234 31*t^26 - 31*t^25 - 31*t^24 - 31*t^23 - 31*t^22 - 31*t^21 - 31*t^20 -
%F A170234 31*t^19 - 31*t^18 - 31*t^17 - 31*t^16 - 31*t^15 - 31*t^14 - 31*t^13 -
%F A170234 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 A170234 - 31*t^4 - 31*t^3 - 31*t^2 - 31*t + 1)
%t A170234 coxG[{40,496,-31}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, May 15 2025 *)
%K A170234 nonn
%O A170234 0,2
%A A170234 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009