cp's OEIS Frontend

A169412 Number of reduced words of length n in Coxeter group on 15 generators S_i with relations (S_i)^2 = (S_i S_j)^32 = I.

%I A169412 #12 May 08 2018 00:55:11
%S A169412 1,15,210,2940,41160,576240,8067360,112943040,1581202560,22136835840,
%T A169412 309915701760,4338819824640,60743477544960,850408685629440,
%U A169412 11905721598812160,166680102383370240,2333521433367183360
%N A169412 Number of reduced words of length n in Coxeter group on 15 generators S_i with relations (S_i)^2 = (S_i S_j)^32 = I.
%C A169412 The initial terms coincide with those of A170734, although the two sequences are eventually different.
%C A169412 First disagreement is at index 32, the difference is 105. - _Klaus Brockhaus_, Jun 27 2011
%C A169412 Computed with Magma using commands similar to those used to compute A154638.
%H A169412 <a href="/index/Rec#order_32">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, -91).
%F A169412 G.f.: (t^32 + 2*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)/(91*t^32 - 13*t^31 - 13*t^30 - 13*t^29 - 13*t^28 - 13*t^27 - 13*t^26 - 13*t^25 - 13*t^24 - 13*t^23 - 13*t^22 - 13*t^21 - 13*t^20 - 13*t^19 - 13*t^18 - 13*t^17 - 13*t^16 - 13*t^15 - 13*t^14 - 13*t^13 - 13*t^12 - 13*t^11 - 13*t^10 - 13*t^9 - 13*t^8 - 13*t^7 - 13*t^6 - 13*t^5 - 13*t^4 - 13*t^3 - 13*t^2 - 13*t + 1).
%F A169412 G.f.: (1+2*sum(k=1..31, x^k)+x^32)/(1-13*sum(k=1..31, x^k)+91*x^32).
%Y A169412 Cf. A170734 (G.f.: (1+x)/(1-14*x) ).
%K A169412 nonn
%O A169412 0,2
%A A169412 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009