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A169548 Number of reduced words of length n in Coxeter group on 7 generators S_i with relations (S_i)^2 = (S_i S_j)^35 = I.

%I A169548 #8 Feb 10 2022 19:23:19
%S A169548 1,7,42,252,1512,9072,54432,326592,1959552,11757312,70543872,
%T A169548 423263232,2539579392,15237476352,91424858112,548549148672,
%U A169548 3291294892032,19747769352192,118486616113152,710919696678912,4265518180073472
%N A169548 Number of reduced words of length n in Coxeter group on 7 generators S_i with relations (S_i)^2 = (S_i S_j)^35 = I.
%C A169548 The initial terms coincide with those of A003949, although the two sequences are eventually different.
%C A169548 Computed with MAGMA using commands similar to those used to compute A154638.
%H A169548 <a href="/index/Rec#order_35">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, -15).
%F A169548 G.f. (t^35 + 2*t^34 + 2*t^33 + 2*t^32 + 2*t^31 + 2*t^30 + 2*t^29 + 2*t^28 +
%F A169548 2*t^27 + 2*t^26 + 2*t^25 + 2*t^24 + 2*t^23 + 2*t^22 + 2*t^21 + 2*t^20 +
%F A169548 2*t^19 + 2*t^18 + 2*t^17 + 2*t^16 + 2*t^15 + 2*t^14 + 2*t^13 + 2*t^12 +
%F A169548 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
%F A169548 + 2*t^2 + 2*t + 1)/(15*t^35 - 5*t^34 - 5*t^33 - 5*t^32 - 5*t^31 - 5*t^30
%F A169548 - 5*t^29 - 5*t^28 - 5*t^27 - 5*t^26 - 5*t^25 - 5*t^24 - 5*t^23 - 5*t^22
%F A169548 - 5*t^21 - 5*t^20 - 5*t^19 - 5*t^18 - 5*t^17 - 5*t^16 - 5*t^15 - 5*t^14
%F A169548 - 5*t^13 - 5*t^12 - 5*t^11 - 5*t^10 - 5*t^9 - 5*t^8 - 5*t^7 - 5*t^6 -
%F A169548 5*t^5 - 5*t^4 - 5*t^3 - 5*t^2 - 5*t + 1)
%t A169548 coxG[{35,15,-5}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Feb 10 2022 *)
%K A169548 nonn
%O A169548 0,2
%A A169548 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009