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A169410 Number of reduced words of length n in Coxeter group on 13 generators S_i with relations (S_i)^2 = (S_i S_j)^32 = I.

%I A169410 #14 Aug 06 2021 17:00:16
%S A169410 1,13,156,1872,22464,269568,3234816,38817792,465813504,5589762048,
%T A169410 67077144576,804925734912,9659108818944,115909305827328,
%U A169410 1390911669927936,16690940039135232,200291280469622784
%N A169410 Number of reduced words of length n in Coxeter group on 13 generators S_i with relations (S_i)^2 = (S_i S_j)^32 = I.
%C A169410 The initial terms coincide with those of A170732, although the two sequences are eventually different.
%C A169410 First disagreement is at index 32, the difference is 78. - _Klaus Brockhaus_, Jun 27 2011
%C A169410 Computed with Magma using commands similar to those used to compute A154638.
%H A169410 <a href="/index/Rec#order_32">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, 11, 11, 11, -66).
%F A169410 G.f.: (t^32 + 2*t^31 + 2*t^30 + 2*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^32 - 11*t^31 - 11*t^30 - 11*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).
%F A169410 G.f.: (1+2*sum(k=1..31, x^k)+x^32)/(1-11*sum(k=1..31, x^k)+66*x^32).
%t A169410 coxG[{32,66,-11}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Aug 06 2021 *)
%Y A169410 Cf. A170732 (G.f.: (1+x)/(1-12*x) ).
%K A169410 nonn
%O A169410 0,2
%A A169410 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009