cp's OEIS Frontend

A170648 Number of reduced words of length n in Coxeter group on 15 generators S_i with relations (S_i)^2 = (S_i S_j)^49 = I.

%I A170648 #10 Aug 24 2024 13:05:31
%S A170648 1,15,210,2940,41160,576240,8067360,112943040,1581202560,22136835840,
%T A170648 309915701760,4338819824640,60743477544960,850408685629440,
%U A170648 11905721598812160,166680102383370240,2333521433367183360
%N A170648 Number of reduced words of length n in Coxeter group on 15 generators S_i with relations (S_i)^2 = (S_i S_j)^49 = I.
%C A170648 The initial terms coincide with those of A170734, although the two sequences are eventually different.
%C A170648 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170648 <a href="/index/Rec#order_49">Index entries for linear recurrences with constant coefficients</a>, signature (13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, -91).
%F A170648 G.f.: (t^49 + 2*t^48 + 2*t^47 + 2*t^46 + 2*t^45 + 2*t^44 + 2*t^43 + 2*t^42 + 2*t^41 + 2*t^40 + 2*t^39 + 2*t^38 + 2*t^37 + 2*t^36 + 2*t^35 + 2*t^34 +
%F A170648 2*t^33 + 2*t^32 + 2*t^31 + 2*t^30 + 2*t^29 + 2*t^28 + 2*t^27 + 2*t^26 +
%F A170648 2*t^25 + 2*t^24 + 2*t^23 + 2*t^22 + 2*t^21 + 2*t^20 + 2*t^19 + 2*t^18 +
%F A170648 2*t^17 + 2*t^16 + 2*t^15 + 2*t^14 + 2*t^13 + 2*t^12 + 2*t^11 + 2*t^10 +
%F A170648 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 +
%F A170648 1)/(91*t^49 - 13*t^48 - 13*t^47 - 13*t^46 - 13*t^45 - 13*t^44 - 13*t^43
%F A170648 - 13*t^42 - 13*t^41 - 13*t^40 - 13*t^39 - 13*t^38 - 13*t^37 - 13*t^36 -
%F A170648 13*t^35 - 13*t^34 - 13*t^33 - 13*t^32 - 13*t^31 - 13*t^30 - 13*t^29 -
%F A170648 13*t^28 - 13*t^27 - 13*t^26 - 13*t^25 - 13*t^24 - 13*t^23 - 13*t^22 -
%F A170648 13*t^21 - 13*t^20 - 13*t^19 - 13*t^18 - 13*t^17 - 13*t^16 - 13*t^15 -
%F A170648 13*t^14 - 13*t^13 - 13*t^12 - 13*t^11 - 13*t^10 - 13*t^9 - 13*t^8 -
%F A170648 13*t^7 - 13*t^6 - 13*t^5 - 13*t^4 - 13*t^3 - 13*t^2 - 13*t + 1).
%F A170648 a(n) = -91*a(n-49) + 13*Sum_{k=1..48} a(n-k). - _Wesley Ivan Hurt_, May 04 2024
%t A170648 coxG[{49,91,-13}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Aug 24 2024 *)
%K A170648 nonn
%O A170648 0,2
%A A170648 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009