A165965 Number of reduced words of length n in Coxeter group on 24 generators S_i with relations (S_i)^2 = (S_i S_j)^10 = I.

1, 24, 552, 12696, 292008, 6716184, 154472232, 3552861336, 81715810728, 1879463646744, 43227663874836, 994236269114880, 22867434189496512, 525950986355068032, 12096872686089474624, 278228071778284843776

Offset

0,2

Comments

The initial terms coincide with those of A170743, 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 (22,22,22,22,22,22,22,22,22,-253).

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)/(253*t^10 - 22*t^9 - 22*t^8 - 22*t^7 - 22*t^6 - 22*t^5 - 22*t^4 - 22*t^3 - 22*t^2 - 22*t + 1).

Maple

seq(coeff(series((1+t)*(1-t^10)/(1-23*t+275*t^10-253*t^11), t, n+1), t, n), n = 0..30); # G. C. Greubel, Sep 26 2019

Mathematica

CoefficientList[Series[(1+t)*(1-t^10)/(1-23*t+275*t^10-253*t^11), {t, 0, 25}], t] (* G. C. Greubel, Apr 18 2016 *)
coxG[{10, 253, -22}] (* The coxG program is at A169452 *) (* G. C. Greubel, Sep 26 2019 *)

Prog

(PARI) my(t='t+O('t^30)); Vec((1+t)*(1-t^10)/(1-23*t+275*t^10-253*t^11)) \\ G. C. Greubel, Sep 26 2019
(Magma) R<t>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1+t)*(1-t^10)/(1-23*t+275*t^10-253*t^11) )); // G. C. Greubel, Sep 26 2019
(Sage)
def A165965_list(prec):
    P.<t> = PowerSeriesRing(ZZ, prec)
    return P((1+t)*(1-t^10)/(1-23*t+275*t^10-253*t^11)).list()
A165965_list(30) # G. C. Greubel, Sep 26 2019
(GAP) a:=[24, 552, 12696, 292008, 6716184, 154472232, 3552861336, 81715810728, 1879463646744, 43227663874836];; for n in [11..30] do a[n]:=22*Sum([1..9], j-> a[n-j]) -253*a[n-10]; od; Concatenation([1], a); # G. C. Greubel, Sep 26 2019

Crossrefs

Sequence in context: A164637 A164959 A165366 * A166418 A166611 A063816

Adjacent sequences: A165962 A165963 A165964 * A165966 A165967 A165968

Keyword

nonn

Author

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

Status

approved