A166026 Number of reduced words of length n in Coxeter group on 30 generators S_i with relations (S_i)^2 = (S_i S_j)^10 = I.

1, 30, 870, 25230, 731670, 21218430, 615334470, 17844699630, 517496289270, 15007392388830, 435214379275635, 12621216998980800, 366015292970077800, 10614443496121659600, 307818861387220827000, 8926746980220492242400

Offset

0,2

Comments

The initial terms coincide with those of A170749, 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 (28,28,28,28,28,28,28,28,28,-406).

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)/(406*t^10 - 28*t^9 - 28*t^8 - 28*t^7 - 28*t^6 - 28*t^5 - 28*t^4 - 28*t^3 - 28*t^2 - 28*t + 1).

Maple

seq(coeff(series((1+t)*(1-t^10)/(1-29*t+334*t^10-406*t^11), t, n+1), t, n), n = 0..30); # G. C. Greubel, Dec 05 2019

Mathematica

CoefficientList[Series[(1+t)*(1-t^10)/(1-29*t+334*t^10-406*t^11), {t, 0, 30}], t] (* G. C. Greubel, Apr 21 2016 *)
coxG[{10, 406, -28}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Sep 13 2020 *)

Prog

(PARI) my(t='t+O('t^30)); Vec((1+t)*(1-t^10)/(1-29*t+334*t^10-406*t^11)) \\ G. C. Greubel, Dec 05 2019
(Magma) R<t>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1+t)*(1-t^10)/(1-29*t+334*t^10-406*t^11) )); // G. C. Greubel, Dec 05 2019
(Sage)
def A166026_list(prec):
    P.<t> = PowerSeriesRing(ZZ, prec)
    return P((1+t)*(1-t^10)/(1-29*t+334*t^10-406*t^11)).list()
A166026_list(30) # G. C. Greubel, Dec 05 2019
(GAP) a:=[30, 870, 25230, 731670, 21218430, 615334470, 17844699630, 517496289270, 15007392388830, 435214379275635];; for n in [11..30] do a[n]:=28*Sum([1..9], j-> a[n-j]) - 406*a[n-10]; od; Concatenation([1], a); # G. C. Greubel, Dec 05 2019

Crossrefs

Sequence in context: A164666 A164983 A165515 * A166424 A166617 A167083

Adjacent sequences: A166023 A166024 A166025 * A166027 A166028 A166029

Keyword

nonn

Author

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

Status

approved