A166129 Number of reduced words of length n in Coxeter group on 33 generators S_i with relations (S_i)^2 = (S_i S_j)^10 = I.

1, 33, 1056, 33792, 1081344, 34603008, 1107296256, 35433480192, 1133871366144, 36283883716608, 1161084278930928, 37154696925772800, 1188950301624189456, 38046409651956777984, 1217485108862063788032, 38959523483568341778432

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, -496).

Formula

G.f.: (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^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).

Maple

seq(coeff(series((1+t)*(1-t^10)/(1-32*t+527*t^10-496*t^11), t, n+1), t, n), n = 0..30); # G. C. Greubel, Mar 11 2020

Mathematica

CoefficientList[Series[(1+t)*(1-t^10)/(1 -32*t +527*t^10 -496*t^11), {t, 0, 30}], t] (* G. C. Greubel, Apr 26 2016 *)
coxG[{496, 10, -31}] (* The coxG program is at A169452 *) (* G. C. Greubel, Mar 11 2020 *)

Prog

(Sage)
def A166129_list(prec):
    P.<t> = PowerSeriesRing(ZZ, prec)
return P( (1+t)*(1-t^10)/(1-32*t+527*t^10-496*t^11) ).list() A166129_list(30) # G. C. Greubel, Mar 11 2020

Crossrefs

Sequence in context: A164669 A165140 A165645 * A166427 A166679 A167086

Adjacent sequences: A166126 A166127 A166128 * A166130 A166131 A166132

Keyword

nonn

Author

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

Status

approved