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A169220 Number of reduced words of length n in Coxeter group on 15 generators S_i with relations (S_i)^2 = (S_i S_j)^28 = I.

%I A169220 #12 Jul 01 2020 19:30:42
%S A169220 1,15,210,2940,41160,576240,8067360,112943040,1581202560,22136835840,
%T A169220 309915701760,4338819824640,60743477544960,850408685629440,
%U A169220 11905721598812160,166680102383370240,2333521433367183360
%N A169220 Number of reduced words of length n in Coxeter group on 15 generators S_i with relations (S_i)^2 = (S_i S_j)^28 = I.
%C A169220 The initial terms coincide with those of A170734, although the two sequences are eventually different.
%C A169220 First disagreement at index 28: a(28) = 132296459669194216956674766274455, A170734(28) = 132296459669194216956674766274560. - _Klaus Brockhaus_, May 24 2011
%C A169220 Computed with Magma using commands similar to those used to compute A154638.
%H A169220 <a href="/index/Rec#order_28">Index entries for linear recurrences with constant coefficients</a>, signature (13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, -91).
%F A169220 G.f.: (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)/(91*t^28 - 13*t^27 - 13*t^26 - 13*t^25 - 13*t^24 - 13*t^23 - 13*t^22 - 13*t^21 - 13*t^20 - 13*t^19 - 13*t^18 - 13*t^17 - 13*t^16 - 13*t^15 - 13*t^14 - 13*t^13 - 13*t^12 - 13*t^11 - 13*t^10 - 13*t^9 - 13*t^8 - 13*t^7 - 13*t^6 - 13*t^5 - 13*t^4 - 13*t^3 - 13*t^2 - 13*t + 1).
%t A169220 coxG[{28,91,-13}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Jul 01 2020 *)
%Y A169220 Cf. A170734 (G.f.: (1+x)/(1-14*x)).
%K A169220 nonn
%O A169220 0,2
%A A169220 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009