A165456 Number of reduced words of length n in Coxeter group on 28 generators S_i with relations (S_i)^2 = (S_i S_j)^9 = I.

1, 28, 756, 20412, 551124, 14880348, 401769396, 10847773692, 292889889684, 7908027021090, 213516729559224, 5764951697823864, 155653695833814360, 4202649787312378584, 113471544252017775096, 3063731694658235867448

Offset

0,2

Comments

The initial terms coincide with those of A170747, 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..695

Index entries for linear recurrences with constant coefficients, signature (26,26,26,26,26,26,26,26,-351).

Formula

G.f.: (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)/(351*t^9 - 26*t^8 - 26*t^7 - 26*t^6 - 26*t^5 - 26*t^4 - 26*t^3 -26*t^2 - 26*t + 1).

Maple

seq(coeff(series((x^9+2*x^8+2*x^7+2*x^6+2*x^5+2*x^4+2*x^3+2*x^2+2*x+1)/( 351*x^9-26*x^8-26*x^7-26*x^6-26*x^5-26*x^4-26*x^3-26*x^2-26*x+1), x, n+1), x, n), n = 0 .. 15); # Muniru A Asiru, Oct 21 2018

Mathematica

CoefficientList[Series[(1+t)*(1-t^9)/(1-27*t+377*t^9-351*t^10), {t, 0, 30}], t] (* G. C. Greubel, Oct 20 2018 *)
coxG[{9, 351, -26}] (* The coxG program is at A169452 *) (* G. C. Greubel, Sep 16 2019 *)

Prog

(PARI) my(t='t+O('t^20)); Vec((1+t)*(1-t^9)/(1-27*t+377*t^9-351*t^10)) \\ G. C. Greubel, Oct 20 2018
(Magma) R<t>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+t)*(1-t^9)/(1-27*t+377*t^9-351*t^10) )); // G. C. Greubel, Oct 20 2018
(Sage)
def A165456_list(prec):
    P.<t> = PowerSeriesRing(ZZ, prec)
    return P((1+t)*(1-t^9)/(1-27*t+377*t^9-351*t^10)).list()
A165456_list(20) # G. C. Greubel, Sep 16 2019
(GAP) a:=[28, 756, 20412, 551124, 14880348, 401769396, 10847773692, 292889889684, 7908027021090];; for n in [10..20] do a[n]:=326*Sum([1..8], j-> a[n-j]) -351*a[n-9]; od; Concatenation([1], a); # G. C. Greubel, Sep 16 2019

Crossrefs

Sequence in context: A164025 A164664 A164970 * A165980 A166422 A166615

Adjacent sequences: A165453 A165454 A165455 * A165457 A165458 A165459

Keyword

nonn,easy

Author

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

Status

approved