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A170064 Number of reduced words of length n in Coxeter group on 7 generators S_i with relations (S_i)^2 = (S_i S_j)^37 = I.

%I A170064 #8 Mar 31 2021 12:28:40
%S A170064 1,7,42,252,1512,9072,54432,326592,1959552,11757312,70543872,
%T A170064 423263232,2539579392,15237476352,91424858112,548549148672,
%U A170064 3291294892032,19747769352192,118486616113152,710919696678912,4265518180073472
%N A170064 Number of reduced words of length n in Coxeter group on 7 generators S_i with relations (S_i)^2 = (S_i S_j)^37 = I.
%C A170064 The initial terms coincide with those of A003949, although the two sequences are eventually different.
%C A170064 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170064 <a href="/index/Rec#order_37">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, -15).
%F A170064 G.f. (t^37 + 2*t^36 + 2*t^35 + 2*t^34 + 2*t^33 + 2*t^32 + 2*t^31 + 2*t^30 +
%F A170064 2*t^29 + 2*t^28 + 2*t^27 + 2*t^26 + 2*t^25 + 2*t^24 + 2*t^23 + 2*t^22 +
%F A170064 2*t^21 + 2*t^20 + 2*t^19 + 2*t^18 + 2*t^17 + 2*t^16 + 2*t^15 + 2*t^14 +
%F A170064 2*t^13 + 2*t^12 + 2*t^11 + 2*t^10 + 2*t^9 + 2*t^8 + 2*t^7 + 2*t^6 +
%F A170064 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(15*t^37 - 5*t^36 - 5*t^35 -
%F A170064 5*t^34 - 5*t^33 - 5*t^32 - 5*t^31 - 5*t^30 - 5*t^29 - 5*t^28 - 5*t^27 -
%F A170064 5*t^26 - 5*t^25 - 5*t^24 - 5*t^23 - 5*t^22 - 5*t^21 - 5*t^20 - 5*t^19 -
%F A170064 5*t^18 - 5*t^17 - 5*t^16 - 5*t^15 - 5*t^14 - 5*t^13 - 5*t^12 - 5*t^11 -
%F A170064 5*t^10 - 5*t^9 - 5*t^8 - 5*t^7 - 5*t^6 - 5*t^5 - 5*t^4 - 5*t^3 - 5*t^2 -
%F A170064 5*t + 1)
%t A170064 coxG[{37,15,-5}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Mar 31 2021 *)
%K A170064 nonn
%O A170064 0,2
%A A170064 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009