A166130 Number of reduced words of length n in Coxeter group on 34 generators S_i with relations (S_i)^2 = (S_i S_j)^10 = I.

1, 34, 1122, 37026, 1221858, 40321314, 1330603362, 43909910946, 1449027061218, 47817893020194, 1577990469665841, 52073685498954240, 1718431621464879552, 56708243508320883072, 1871372035773924450624, 61755277180517572075776

Offset

0,2

Comments

The initial terms coincide with those of A170753, 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 (32, 32, 32, 32, 32, 32, 32, 32, 32, -528).

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)/(528*t^10 - 32*t^9 - 32*t^8 - 32*t^7 - 32*t^6 - 32*t^5 - 32*t^4 - 32*t^3 - 32*t^2 - 32*t + 1).

Maple

seq(coeff(series((1+t)*(1-t^10)/(1-33*t+560*t^10-528*t^11), t, n+1), t, n), n = 0 .. 30); # G. C. Greubel, Mar 11 2020

Mathematica

CoefficientList[Series[(1+t)*(1-t^10)/(1-33*t+560*t^10-528*t^11), {t, 0, 30}], t] (* G. C. Greubel, Apr 26 2016 *)
coxG[{528, 10, -32}] (* The coxG program is at A169452 *) (* G. C. Greubel, Mar 11 2020 *)

Prog

(Sage)
def A166130_list(prec):
    P.<t> = PowerSeriesRing(ZZ, prec)
return P( (1+t)*(1-t^10)/(1-33*t+560*t^10-528*t^11) ).list() A166130_list(30) # G. C. Greubel, Mar 11 2020

Crossrefs

Sequence in context: A164670 A165166 A165649 * A166428 A166682 A167087

Adjacent sequences: A166127 A166128 A166129 * A166131 A166132 A166133

Keyword

nonn

Author

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

Status

approved