A169334 Number of reduced words of length n in Coxeter group on 33 generators S_i with relations (S_i)^2 = (S_i S_j)^30 = I.

1, 33, 1056, 33792, 1081344, 34603008, 1107296256, 35433480192, 1133871366144, 36283883716608, 1161084278931456, 37154696925806592, 1188950301625810944, 38046409652025950208, 1217485108864830406656, 38959523483674573012992

Offset: 0

Author

John Cannon and N. J. A. Sloane, Dec 03 2009

Keywords

• nonn

Comments

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

First disagreement at index 30: a(30) = 1471849183103021127341357405994791859394706928, A170752(30) = 1471849183103021127341357405994791859394707456. - Klaus Brockhaus, Jun 23 2011

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

Links

• Index entries for linear recurrences with constant coefficients, 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, 31, 31, 31, 31, -496).

Crossrefs

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

Programs

Mathematica

With[{num=Total[2t^Range[29]]+t^30+1,den=Total[-31 t^Range[29]]+ 496t^30+ 1},CoefficientList[Series[num/den,{t,0,30}],t]] (* Harvey P. Dale, Feb 27 2013 *)

Formula

G.f.: (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)/(496*t^30 - 31*t^29 - 31*t^28 - 31*t^27 - 31*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).