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A168881 Number of reduced words of length n in Coxeter group on 12 generators S_i with relations (S_i)^2 = (S_i S_j)^21 = I.

%I A168881 #12 Sep 08 2022 08:45:49
%S A168881 1,12,132,1452,15972,175692,1932612,21258732,233846052,2572306572,
%T A168881 28295372292,311249095212,3423740047332,37661140520652,
%U A168881 414272545727172,4556998002998892,50126978032987812,551396758362865932
%N A168881 Number of reduced words of length n in Coxeter group on 12 generators S_i with relations (S_i)^2 = (S_i S_j)^21 = I.
%C A168881 The initial terms coincide with those of A003954, although the two sequences are eventually different.
%C A168881 First disagreement at index 21: a(21) = 8072999939190720110346, A003954(21) = 8072999939190720110412. - Klaus Brockhaus, Apr 05 2011
%C A168881 Computed with MAGMA using commands similar to those used to compute A154638.
%H A168881 G. C. Greubel, <a href="/A168881/b168881.txt">Table of n, a(n) for n = 0..950</a>
%H A168881 <a href="/index/Rec#order_21">Index entries for linear recurrences with constant coefficients</a>, signature (10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,-55).
%F A168881 G.f.: (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)/(55*t^21 - 10*t^20 - 10*t^19 - 10*t^18 - 10*t^17 - 10*t^16 - 10*t^15 - 10*t^14 - 10*t^13 - 10*t^12 - 10*t^11 - 10*t^10 - 10*t^9 - 10*t^8 - 10*t^7 - 10*t^6 - 10*t^5 - 10*t^4 - 10*t^3 - 10*t^2 - 10*t + 1).
%F A168881 G.f.: (1+t)*(1-t^21)/(1 -11*t +65*t^21 -55*t^22). - _G. C. Greubel_, Sep 25 2019
%p A168881 seq(coeff(series((1+t)*(1-t^21)/(1-11*t+65*t^21-55*t^22), t, n+1), t, n), n = 0..20); # _G. C. Greubel_, Sep 25 2019
%t A168881 CoefficientList[Series[(1+t)*(1-t^21)/(1-11*t+65*t^21-55*t^22), {t, 0, 20}], t] (* _G. C. Greubel_, Sep 25 2019 *)
%t A168881 coxG[{21, 55, -10}] (* The coxG program is at A169452 *) (* _G. C. Greubel_, Sep 25 2019 *)
%o A168881 (PARI) my(t='t+O('t^20)); Vec((1+t)*(1-t^21)/(1-11*t+65*t^21-55*t^22)) \\ _G. C. Greubel_, Sep 25 2019
%o A168881 (Magma) R<t>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+t)*(1-t^21)/(1-11*t+65*t^21-55*t^22) )); // _G. C. Greubel_, Sep 25 2019
%o A168881 (Sage)
%o A168881 def A168881_list(prec):
%o A168881     P.<t> = PowerSeriesRing(ZZ, prec)
%o A168881     return P((1+t)*(1-t^21)/(1-11*t+65*t^21-55*t^22)).list()
%o A168881 A168881_list(20) # _G. C. Greubel_, Sep 25 2019
%Y A168881 Cf. A003954 (G.f.: (1+x)/(1-11*x)).
%K A168881 nonn
%O A168881 0,2
%A A168881 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009