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URL: https://oeis.org/A164664

⇱ A164664 - OEIS

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A164664
Number of reduced words of length n in Coxeter group on 28 generators S_i with relations (S_i)^2 = (S_i S_j)^7 = I.
2
1, 28, 756, 20412, 551124, 14880348, 401769396, 10847773314, 292889869272, 7908026195160, 213516699839352, 5764950695053368, 155653663349994264, 4202648764205784984, 113471512684966713186, 3063730735882188973692
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.
FORMULA
G.f.: (t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(351*t^7 - 26*t^6 - 26*t^5 - 26*t^4 - 26*t^3 - 26*t^2 - 26*t + 1).
MAPLE
seq(coeff(series((1+t)*(1-t^7)/(1-27*t+377*t^7-351*t^8), t, n+1), t, n), n = 0 .. 30); # G. C. Greubel, Sep 15 2019
MATHEMATICA
CoefficientList[Series[(t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(351*t^7 - 26*t^6 - 26*t^5 - 26*t^4 - 26*t^3 - 26*t^2 - 26*t + 1), {t, 0, 20}], t] (* Wesley Ivan Hurt, Apr 25 2017 *)
coxG[{7, 351, -26}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Aug 13 2018 *)
PROG
(PARI) my(t='t+O('t^20)); Vec((1+t)*(1-t^7)/(1-27*t+377*t^7-351*t^8)) \\ G. C. Greubel, Sep 15 2019
(Magma) R<t>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+t)*(1-t^7)/(1-27*t+377*t^7-351*t^8) )); // G. C. Greubel, Sep 15 2019
(SageMath)
def A164664_list(prec):
P.<t> = PowerSeriesRing(ZZ, prec)
return P((1+t)*(1-t^7)/(1-27*t+377*t^7-351*t^8)).list()
A164664_list(20) # G. C. Greubel, Sep 15 2019
(GAP) a:=[28, 756, 20412, 551124, 14880348, 401769396, 10847773314];; for n in [8..30] do a[n]:=26*(a[n-1] +a[n-2]+a[n-3]+a[n-4]+a[n-5]+a[n-6]) -351*a[n-7]; od; Concatenation([1], a); # G. C. Greubel, Sep 15 2019
CROSSREFS
Sequence in context: A163187 A163548 A164025 * A164970 A165456 A165980
KEYWORD
nonn
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved