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A167935 Number of reduced words of length n in Coxeter group on 22 generators S_i with relations (S_i)^2 = (S_i S_j)^16 = I.

%I A167935 #21 Sep 08 2022 08:45:48
%S A167935 1,22,462,9702,203742,4278582,89850222,1886854662,39623947902,
%T A167935 832102905942,17474161024782,366957381520422,7706105011928862,
%U A167935 161828205250506102,3398392310260628142,71366238515473190982
%N A167935 Number of reduced words of length n in Coxeter group on 22 generators S_i with relations (S_i)^2 = (S_i S_j)^16 = I.
%C A167935 The initial terms coincide with those of A170741, although the two sequences are eventually different.
%C A167935 Computed with MAGMA using commands similar to those used to compute A154638.
%H A167935 G. C. Greubel, <a href="/A167935/b167935.txt">Table of n, a(n) for n = 0..500</a>
%H A167935 <a href="/index/Rec#order_16">Index entries for linear recurrences with constant coefficients</a>, signature (20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, -210).
%F A167935 G.f.: (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)/(210*t^16 - 20*t^15 - 20*t^14 - 20*t^13 - 20*t^12 - 20*t^11 - 20*t^10 - 20*t^9 - 20*t^8 - 20*t^7 - 20*t^6 - 20*t^5 - 20*t^4 - 20*t^3 - 20*t^2 - 20*t + 1).
%F A167935 G.f.: (1+x)*(1-x^16)/(1 - 21*x + 230*x^16 - 210*x^17). - _G. C. Greubel_, Apr 26 2019
%F A167935 a(n) = -210*a(n-16) + 20*Sum_{k=1..15} a(n-k). - _Wesley Ivan Hurt_, May 06 2021
%t A167935 CoefficientList[Series[(1+x)*(1-x^16)/(1-21*x+230*x^16-210*x^17), {x, 0, 20}], x] (* _G. C. Greubel_, Jul 01 2016, modified Apr 26 2019 *)
%t A167935 coxG[{16, 210, -20}] (* The coxG program is at A169452 *) (* _G. C. Greubel_, Apr 26 2019 *)
%o A167935 (PARI) my(x='x+O('x^20)); Vec((1+x)*(1-x^16)/(1-21*x+230*x^16-210*x^17)) \\ _G. C. Greubel_, Apr 26 2019
%o A167935 (Magma) R<x>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^16)/(1-21*x+230*x^16-210*x^17) )); // _G. C. Greubel_, Apr 26 2019
%o A167935 (Sage) ((1+x)*(1-x^16)/(1-21*x+230*x^16-210*x^17)).series(x, 20).coefficients(x, sparse=False) # _G. C. Greubel_, Apr 26 2019
%Y A167935 Cf. A154638, A170741.
%K A167935 nonn
%O A167935 0,2
%A A167935 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009