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A169266 Number of reduced words of length n in Coxeter group on 13 generators S_i with relations (S_i)^2 = (S_i S_j)^29 = I.

%I A169266 #12 Aug 02 2023 16:01:53
%S A169266 1,13,156,1872,22464,269568,3234816,38817792,465813504,5589762048,
%T A169266 67077144576,804925734912,9659108818944,115909305827328,
%U A169266 1390911669927936,16690940039135232,200291280469622784
%N A169266 Number of reduced words of length n in Coxeter group on 13 generators S_i with relations (S_i)^2 = (S_i S_j)^29 = I.
%C A169266 The initial terms coincide with those of A170732, although the two sequences are eventually different.
%C A169266 First disagreement at index 29: a(29) = 21429806106923663071363567976370, A170732(29) = 21429806106923663071363567976448. - _Klaus Brockhaus_, Jun 03 2011
%C A169266 Computed with Magma using commands similar to those used to compute A154638.
%H A169266 <a href="/index/Rec#order_29">Index entries for linear recurrences with constant coefficients</a>, signature (11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, -66).
%F A169266 G.f.: (t^29 + 2*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)/(66*t^29 - 11*t^28 - 11*t^27 - 11*t^26 - 11*t^25 - 11*t^24 - 11*t^23 - 11*t^22 - 11*t^21 - 11*t^20 - 11*t^19 - 11*t^18 - 11*t^17 - 11*t^16 - 11*t^15 - 11*t^14 - 11*t^13 - 11*t^12 - 11*t^11 - 11*t^10 - 11*t^9 - 11*t^8 - 11*t^7 - 11*t^6 - 11*t^5 - 11*t^4 - 11*t^3 - 11*t^2 - 11*t + 1).
%t A169266 coxG[{29,66,-11}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Aug 02 2023 *)
%Y A169266 Cf. A170732 (G.f.: (1+x)/(1-12*x)).
%K A169266 nonn
%O A169266 0,2
%A A169266 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009