cp's OEIS Frontend

A170304 Number of reduced words of length n in Coxeter group on 7 generators S_i with relations (S_i)^2 = (S_i S_j)^42 = I.

%I A170304 #8 Jun 27 2025 18:58:22
%S A170304 1,7,42,252,1512,9072,54432,326592,1959552,11757312,70543872,
%T A170304 423263232,2539579392,15237476352,91424858112,548549148672,
%U A170304 3291294892032,19747769352192,118486616113152,710919696678912,4265518180073472
%N A170304 Number of reduced words of length n in Coxeter group on 7 generators S_i with relations (S_i)^2 = (S_i S_j)^42 = I.
%C A170304 The initial terms coincide with those of A003949, although the two sequences are eventually different.
%C A170304 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170304 <a href="/index/Rec#order_42">Index entries for linear recurrences with constant coefficients</a>, signature (5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, -15).
%F A170304 G.f. (t^42 + 2*t^41 + 2*t^40 + 2*t^39 + 2*t^38 + 2*t^37 + 2*t^36 + 2*t^35 +
%F A170304 2*t^34 + 2*t^33 + 2*t^32 + 2*t^31 + 2*t^30 + 2*t^29 + 2*t^28 + 2*t^27 +
%F A170304 2*t^26 + 2*t^25 + 2*t^24 + 2*t^23 + 2*t^22 + 2*t^21 + 2*t^20 + 2*t^19 +
%F A170304 2*t^18 + 2*t^17 + 2*t^16 + 2*t^15 + 2*t^14 + 2*t^13 + 2*t^12 + 2*t^11 +
%F A170304 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 +
%F A170304 2*t + 1)/(15*t^42 - 5*t^41 - 5*t^40 - 5*t^39 - 5*t^38 - 5*t^37 - 5*t^36
%F A170304 - 5*t^35 - 5*t^34 - 5*t^33 - 5*t^32 - 5*t^31 - 5*t^30 - 5*t^29 - 5*t^28
%F A170304 - 5*t^27 - 5*t^26 - 5*t^25 - 5*t^24 - 5*t^23 - 5*t^22 - 5*t^21 - 5*t^20
%F A170304 - 5*t^19 - 5*t^18 - 5*t^17 - 5*t^16 - 5*t^15 - 5*t^14 - 5*t^13 - 5*t^12
%F A170304 - 5*t^11 - 5*t^10 - 5*t^9 - 5*t^8 - 5*t^7 - 5*t^6 - 5*t^5 - 5*t^4 -
%F A170304 5*t^3 - 5*t^2 - 5*t + 1)
%t A170304 coxG[{42,15,-5}] (* _Harvey P. Dale_, Jun 27 2025 *)
%K A170304 nonn
%O A170304 0,2
%A A170304 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009