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A167827 Number of reduced words of length n in Coxeter group on 38 generators S_i with relations (S_i)^2 = (S_i S_j)^15 = I.

%I A167827 #16 Aug 11 2025 11:37:21
%S A167827 1,38,1406,52022,1924814,71218118,2635070366,97497603542,
%T A167827 3607411331054,133474219248998,4938546112212926,182726206151878262,
%U A167827 6760869627619495694,250152176221921340678,9255630520211089605086
%N A167827 Number of reduced words of length n in Coxeter group on 38 generators S_i with relations (S_i)^2 = (S_i S_j)^15 = I.
%C A167827 The initial terms coincide with those of A170757, although the two sequences start to be different at a(15).
%C A167827 Computed with MAGMA using commands similar to those used to compute A154638.
%H A167827 G. C. Greubel, <a href="/A167827/b167827.txt">Table of n, a(n) for n = 0..500</a>
%H A167827 <a href="/index/Rec#order_15">Index entries for linear recurrences with constant coefficients</a>, signature (36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, -666).
%F A167827 G.f.: (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)/(666*t^15 - 36*t^14 - 36*t^13 - 36*t^12 - 36*t^11 - 36*t^10 - 36*t^9 - 36*t^8 - 36*t^7 - 36*t^6 - 36*t^5 - 36*t^4 - 36*t^3 - 36*t^2 - 36*t + 1).
%p A167827 (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)/(666*t^15 - 36*t^14 - 36*t^13 - 36*t^12 - 36*t^11 - 36*t^10 - 36*t^9 - 36*t^8 - 36*t^7 - 36*t^6 - 36*t^5 - 36*t^4 - 36*t^3 - 36*t^2 - 36*t + 1) ;
%p A167827 taylor(%,t=0,64) ;
%p A167827 gfun[seriestolist](%) ; # _R. J. Mathar_, Apr 12 2019
%t A167827 CoefficientList[Series[(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)/(666*t^15 - 36*t^14 - 36*t^13 - 36*t^12 - 36*t^11 - 36*t^10 - 36*t^9 - 36*t^8 - 36*t^7 - 36*t^6 - 36*t^5 - 36*t^4 - 36*t^3 - 36*t^2 - 36*t + 1), {t, 0, 50}], t] (* _G. C. Greubel_, Jun 27 2016 *)
%t A167827 coxG[{15,666,-36}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Aug 11 2025 *)
%K A167827 nonn
%O A167827 0,2
%A A167827 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009