A169390 - OEIS

%I #26 Oct 11 2024 23:02:55

%S 1,41,1640,65600,2624000,104960000,4198400000,167936000000,

%T 6717440000000,268697600000000,10747904000000000,429916160000000000,

%U 17196646400000000000,687865856000000000000,27514634240000000000000

%N Number of reduced words of length n in Coxeter group on 41 generators S_i with relations (S_i)^2 = (S_i S_j)^31 = I.

%C The initial terms coincide with those of A170760, although the two sequences are eventually different.

%C First disagreement at index 31: a(31) = 47269781688880726015999999999999999999999999999180, A170760(31) = 47269781688880726016000000000000000000000000000000. - _Klaus Brockhaus_, Jun 17 2011

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

%H Vincenzo Librandi, <a href="/A169390/b169390.txt">Table of n, a(n) for n = 0..100</a>

%H <a href="/index/Rec#order_31">Index entries for linear recurrences with constant coefficients</a>, signature (39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, -780).

%F G.f.: (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)/(780*t^31 - 39*t^30 - 39*t^29 - 39*t^28 - 39*t^27 - 39*t^26 - 39*t^25 - 39*t^24 - 39*t^23 - 39*t^22 - 39*t^21 - 39*t^20 - 39*t^19 - 39*t^18 - 39*t^17 - 39*t^16 - 39*t^15 - 39*t^14 - 39*t^13 - 39*t^12 - 39*t^11 - 39*t^10 - 39*t^9 - 39*t^8 - 39*t^7 - 39*t^6 - 39*t^5 - 39*t^4 - 39*t^3 - 39*t^2 - 39*t + 1).

%t With[{num=Total[2t^Range[30]]+t^31+1,den=Total[-39 t^Range[30]]+780 t^31+ 1}, CoefficientList[Series[num/den,{t,0,30}],t]] (* _Harvey P. Dale_, Feb 04 2012 *)

%Y Cf. A170760 (G.f.: (1+x)/(1-40*x)).

%K nonn

%O 0,2

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