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

0,2

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

Table of n, a(n) for n=0..15.

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).

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).

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 *)

Crossrefs

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

Sequence in context: A169190 A169238 A169286 * A169382 A169430 A169478

Adjacent sequences: A169331 A169332 A169333 * A169335 A169336 A169337

Keyword

nonn

Author

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

Status

approved