cp's OEIS Frontend

A170550 Number of reduced words of length n in Coxeter group on 13 generators S_i with relations (S_i)^2 = (S_i S_j)^47 = I.

%I A170550 #8 Jul 14 2025 16:36:39
%S A170550 1,13,156,1872,22464,269568,3234816,38817792,465813504,5589762048,
%T A170550 67077144576,804925734912,9659108818944,115909305827328,
%U A170550 1390911669927936,16690940039135232,200291280469622784
%N A170550 Number of reduced words of length n in Coxeter group on 13 generators S_i with relations (S_i)^2 = (S_i S_j)^47 = I.
%C A170550 The initial terms coincide with those of A170732, although the two sequences are eventually different.
%C A170550 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170550 <a href="/index/Rec#order_47">Index entries for linear recurrences with constant coefficients</a>, signature (11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, -66).
%F A170550 G.f. (t^47 + 2*t^46 + 2*t^45 + 2*t^44 + 2*t^43 + 2*t^42 + 2*t^41 + 2*t^40 +
%F A170550 2*t^39 + 2*t^38 + 2*t^37 + 2*t^36 + 2*t^35 + 2*t^34 + 2*t^33 + 2*t^32 +
%F A170550 2*t^31 + 2*t^30 + 2*t^29 + 2*t^28 + 2*t^27 + 2*t^26 + 2*t^25 + 2*t^24 +
%F A170550 2*t^23 + 2*t^22 + 2*t^21 + 2*t^20 + 2*t^19 + 2*t^18 + 2*t^17 + 2*t^16 +
%F A170550 2*t^15 + 2*t^14 + 2*t^13 + 2*t^12 + 2*t^11 + 2*t^10 + 2*t^9 + 2*t^8 +
%F A170550 2*t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(66*t^47 -
%F A170550 11*t^46 - 11*t^45 - 11*t^44 - 11*t^43 - 11*t^42 - 11*t^41 - 11*t^40 -
%F A170550 11*t^39 - 11*t^38 - 11*t^37 - 11*t^36 - 11*t^35 - 11*t^34 - 11*t^33 -
%F A170550 11*t^32 - 11*t^31 - 11*t^30 - 11*t^29 - 11*t^28 - 11*t^27 - 11*t^26 -
%F A170550 11*t^25 - 11*t^24 - 11*t^23 - 11*t^22 - 11*t^21 - 11*t^20 - 11*t^19 -
%F A170550 11*t^18 - 11*t^17 - 11*t^16 - 11*t^15 - 11*t^14 - 11*t^13 - 11*t^12 -
%F A170550 11*t^11 - 11*t^10 - 11*t^9 - 11*t^8 - 11*t^7 - 11*t^6 - 11*t^5 - 11*t^4
%F A170550 - 11*t^3 - 11*t^2 - 11*t + 1)
%t A170550 coxG[{47,66,-11}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Jul 14 2025 *)
%K A170550 nonn
%O A170550 0,2
%A A170550 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009