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A169374 Number of reduced words of length n in Coxeter group on 25 generators S_i with relations (S_i)^2 = (S_i S_j)^31 = I.

%I A169374 #15 Oct 11 2024 06:57:50
%S A169374 1,25,600,14400,345600,8294400,199065600,4777574400,114661785600,
%T A169374 2751882854400,66045188505600,1585084524134400,38042028579225600,
%U A169374 913008685901414400,21912208461633945600,525893003079214694400
%N A169374 Number of reduced words of length n in Coxeter group on 25 generators S_i with relations (S_i)^2 = (S_i S_j)^31 = I.
%C A169374 The initial terms coincide with those of A170744, although the two sequences are eventually different.
%C A169374 First disagreement at index 31: a(31) = 6372021903844030065694345748172719416934100, A170744(31) = 6372021903844030065694345748172719416934400. - _Klaus Brockhaus_, Jun 17 2011
%C A169374 Computed with Magma using commands similar to those used to compute A154638.
%H A169374 <a href="/index/Rec#order_31">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, -276).
%F A169374 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)/(276*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).
%t A169374 coxG[{31,276,-23}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Feb 10 2015 *)
%Y A169374 Cf. A170744 (G.f.: (1+x)/(1-24*x)).
%K A169374 nonn
%O A169374 0,2
%A A169374 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009