cp's OEIS Frontend

A169422 Number of reduced words of length n in Coxeter group on 25 generators S_i with relations (S_i)^2 = (S_i S_j)^32 = I.

%I A169422 #12 May 08 2018 01:00:08
%S A169422 1,25,600,14400,345600,8294400,199065600,4777574400,114661785600,
%T A169422 2751882854400,66045188505600,1585084524134400,38042028579225600,
%U A169422 913008685901414400,21912208461633945600,525893003079214694400
%N A169422 Number of reduced words of length n in Coxeter group on 25 generators S_i with relations (S_i)^2 = (S_i S_j)^32 = I.
%C A169422 The initial terms coincide with those of A170744, although the two sequences are eventually different.
%C A169422 First disagreement is at index 32, the difference is 300. - _Klaus Brockhaus_, Jun 27 2011
%C A169422 Computed with Magma using commands similar to those used to compute A154638.
%H A169422 <a href="/index/Rec#order_32">Index entries for linear recurrences with constant coefficients</a>, signature (23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, -276).
%F A169422 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)/(276*t^32 - 23*t^31 - 23*t^30 - 23*t^29 - 23*t^28 - 23*t^27 - 23*t^26 - 23*t^25 - 23*t^24 - 23*t^23 - 23*t^22 - 23*t^21 - 23*t^20 - 23*t^19 - 23*t^18 - 23*t^17 - 23*t^16 - 23*t^15 - 23*t^14 - 23*t^13 - 23*t^12 - 23*t^11 - 23*t^10 - 23*t^9 - 23*t^8 - 23*t^7 - 23*t^6 - 23*t^5 - 23*t^4 - 23*t^3 - 23*t^2 - 23*t + 1).
%F A169422 G.f.: (1+2*sum(k=1..31, x^k)+x^32)/(1-23*sum(k=1..31, x^k)+276*x^32).
%Y A169422 Cf. A170744 (G.f.: (1+x)/(1-24*x) ).
%K A169422 nonn
%O A169422 0,2
%A A169422 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009