A169142 - OEIS

%I #10 Mar 16 2019 15:31:06

%S 1,33,1056,33792,1081344,34603008,1107296256,35433480192,

%T 1133871366144,36283883716608,1161084278931456,37154696925806592,

%U 1188950301625810944,38046409652025950208,1217485108864830406656,38959523483674573012992

%N Number of reduced words of length n in Coxeter group on 33 generators S_i with relations (S_i)^2 = (S_i S_j)^26 = I.

%C The initial terms coincide with those of A170752, although the two sequences are eventually different.

%C First disagreement at index 26: a(26) = 1403664763548871161786420255656043871728, A170752(26) = 1403664763548871161786420255656043872256. - Klaus Brockhaus, Apr 30 2011

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

%H <a href="/index/Rec#order_26">Index entries for linear recurrences with constant coefficients</a>, signature (31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, -496).

%F G.f.: (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)/(496*t^26 - 31*t^25 - 31*t^24 - 31*t^23 - 31*t^22 - 31*t^21 - 31*t^20 - 31*t^19 - 31*t^18 - 31*t^17 - 31*t^16 - 31*t^15 - 31*t^14 - 31*t^13 - 31*t^12 - 31*t^11 - 31*t^10 - 31*t^9 - 31*t^8 - 31*t^7 - 31*t^6 - 31*t^5 - 31*t^4 - 31*t^3 - 31*t^2 - 31*t + 1).

%t coxG[{26,496,-31}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Mar 16 2019 *)

%Y Cf. A170752 (G.f.: (1+x)/(1-32*x)).

%K nonn

%O 0,2

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