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A169278 Number of reduced words of length n in Coxeter group on 25 generators S_i with relations (S_i)^2 = (S_i S_j)^29 = I.

%I A169278 #12 Mar 21 2025 15:35:33
%S A169278 1,25,600,14400,345600,8294400,199065600,4777574400,114661785600,
%T A169278 2751882854400,66045188505600,1585084524134400,38042028579225600,
%U A169278 913008685901414400,21912208461633945600,525893003079214694400
%N A169278 Number of reduced words of length n in Coxeter group on 25 generators S_i with relations (S_i)^2 = (S_i S_j)^29 = I.
%C A169278 The initial terms coincide with those of A170744, although the two sequences are eventually different.
%C A169278 First disagreement at index 29: a(29) = 11062538027506996641830461368355415654100, A170744(29) = 11062538027506996641830461368355415654400. - _Klaus Brockhaus_, Jun 03 2011
%C A169278 Computed with Magma using commands similar to those used to compute A154638.
%H A169278 <a href="/index/Rec#order_29">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, -276).
%F A169278 G.f.: (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^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).
%t A169278 coxG[{29,276,-23}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Mar 21 2025 *)
%Y A169278 Cf. A170744 (G.f.: (1+x)/(1-24*x)).
%K A169278 nonn
%O A169278 0,2
%A A169278 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009