A167695 - OEIS

%I #15 Jun 13 2026 14:19:52

%S 1,24,552,12696,292008,6716184,154472232,3552861336,81715810728,

%T 1879463646744,43227663875112,994236269127576,22867434189934248,

%U 525950986368487704,12096872686475217192,278228071788929995140

%N Number of reduced words of length n in Coxeter group on 24 generators S_i with relations (S_i)^2 = (S_i S_j)^15 = I.

%C The initial terms coincide with those of A170743, although the two sequences are eventually different.

%C Computed with Magma using commands similar to those used to compute A154638.

%H G. C. Greubel, <a href="/A167695/b167695.txt">Table of n, a(n) for n = 0..500</a>

%H <a href="/index/Rec#order_15">Index entries for linear recurrences with constant coefficients</a>, signature (22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, -253).

%F 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)/(253*t^15 - 22*t^14 - 22*t^13 - 22*t^12 - 22*t^11 - 22*t^10 - 22*t^9 - 22*t^8 - 22*t^7 - 22*t^6 - 22*t^5 - 22*t^4 - 22*t^3 - 22*t^2 - 22*t + 1).

%t 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)/(253*t^15 - 22*t^14 - 22*t^13 - 22*t^12 - 22*t^11 - 22*t^10 - 22*t^9 - 22*t^8 - 22*t^7 - 22*t^6 - 22*t^5 - 22*t^4 - 22*t^3 - 22*t^2 - 22*t + 1), {t, 0, 50}], t] (* _G. C. Greubel_, Jun 20 2016 *)

%t coxG[{15,253,-22}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Aug 27 2020 *)

%o (PARI) first(n)=Vec((1+x^5+x^10)*(1+x+x^2+x^3+x^4)*(1+x)/(1-22*x-22*x^2-22*x^3-22*x^4-22*x^5-22*x^6-22*x^7-22*x^8-22*x^9-22*x^10-22*x^11-22*x^12-22*x^13-22*x^14+253*x^15)+O(x^(n+1))) \\ _Charles R Greathouse IV_, Jun 13 2026

%Y Cf. A170743, A154638.

%K nonn,easy,changed

%O 0,2

%A _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009