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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
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
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
(SageMath)
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
KEYWORD
nonn,easy
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved