A166679 Number of reduced words of length n in Coxeter group on 33 generators S_i with relations (S_i)^2 = (S_i S_j)^12 = I.

1, 33, 1056, 33792, 1081344, 34603008, 1107296256, 35433480192, 1133871366144, 36283883716608, 1161084278931456, 37154696925806592, 1188950301625810416, 38046409652025916416, 1217485108864828785168, 38959523483674503840768

Offset

0,2

Comments

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

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

Links

G. C. Greubel, Table of n, a(n) for n = 0..500

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

Formula

G.f.: (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^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

CoefficientList[Series[(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^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, 0, 50}], t] (* G. C. Greubel, May 23 2016 *)
coxG[{12, 496, -31}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Jul 21 2021 *)

Crossrefs

Sequence in context: A165645 A166129 A166427 * A167086 A167391 A167765

Adjacent sequences: A166676 A166677 A166678 * A166680 A166681 A166682

Keyword

nonn

Author

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

Status

approved