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A169392 Number of reduced words of length n in Coxeter group on 43 generators S_i with relations (S_i)^2 = (S_i S_j)^31 = I.

%I A169392 #16 Oct 11 2024 23:02:47
%S A169392 1,43,1806,75852,3185784,133802928,5619722976,236028364992,
%T A169392 9913191329664,416354035845888,17486869505527296,734448519232146432,
%U A169392 30846837807750150144,1295567187925506306048,54413821892871264854016
%N A169392 Number of reduced words of length n in Coxeter group on 43 generators S_i with relations (S_i)^2 = (S_i S_j)^31 = I.
%C A169392 The initial terms coincide with those of A170762, although the two sequences are eventually different.
%C A169392 First disagreement at index 31: a(31) = 214262993157260018632987928501503630744371836484729, A170762(31) = 214262993157260018632987928501503630744371836485632. - _Klaus Brockhaus_, Jun 17 2011
%C A169392 Computed with Magma using commands similar to those used to compute A154638.
%H A169392 <a href="/index/Rec#order_31">Index entries for linear recurrences with constant coefficients</a>, signature (41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, -861).
%F A169392 G.f.: (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)/(861*t^31 - 41*t^30 - 41*t^29 - 41*t^28 - 41*t^27 - 41*t^26 - 41*t^25 - 41*t^24 - 41*t^23 - 41*t^22 - 41*t^21 - 41*t^20 - 41*t^19 - 41*t^18 - 41*t^17 - 41*t^16 - 41*t^15 - 41*t^14 - 41*t^13 - 41*t^12 - 41*t^11 - 41*t^10 - 41*t^9 - 41*t^8 - 41*t^7 - 41*t^6 - 41*t^5 - 41*t^4 - 41*t^3 - 41*t^2 - 41*t + 1).
%t A169392 coxG[{31,861,-41}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Dec 18 2018 *)
%Y A169392 Cf. A170762 (G.f.: (1+x)/(1-42*x)).
%K A169392 nonn
%O A169392 0,2
%A A169392 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009