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A165967
Number of reduced words of length n in Coxeter group on 25 generators S_i with relations (S_i)^2 = (S_i S_j)^10 = I.
1
1, 25, 600, 14400, 345600, 8294400, 199065600, 4777574400, 114661785600, 2751882854400, 66045188505300, 1585084524120000, 38042028578707500, 913008685884840000, 21912208461136800000, 525893003064898560000
OFFSET
0,2
COMMENTS
The initial terms coincide with those of A170744, although the two sequences are eventually different.
Computed with Magma using commands similar to those used to compute A154638.
LINKS
Index entries for linear recurrences with constant coefficients, signature (23,23,23,23,23,23,23,23,23,-276).
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)/(276*t^10 - 23*t^9 - 23*t^8 - 23*t^7 - 23*t^6 - 23*t^5 - 23*t^4 - 23*t^3 - 23*t^2 - 23*t + 1).
MAPLE
seq(coeff(series((1+t)*(1-t^10)/(1-24*t+299*t^10-276*t^11), t, n+1), t, n), n = 0..30); # G. C. Greubel, Sep 26 2019
MATHEMATICA
CoefficientList[Series[(1+t)*(1-t^10)/(1-24*t+299*t^10-276*t^11), {t, 0, 25}], t] (* G. C. Greubel, Apr 18 2016 *)
coxG[{10, 276, -23}] (* 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)/(1-24*t+299*t^10-276*t^11)) \\ G. C. Greubel, Sep 26 2019
(Magma) R<t>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1+t)*(1-t^10)/(1-24*t+299*t^10-276*t^11) )); // G. C. Greubel, Sep 26 2019
(SageMath)
def A165967_list(prec):
P.<t> = PowerSeriesRing(ZZ, prec)
return P((1+t)*(1-t^10)/(1-24*t+299*t^10-276*t^11)).list()
A165967_list(30) # G. C. Greubel, Sep 26 2019
(GAP) a:=[25, 600, 14400, 345600, 8294400, 199065600, 4777574400, 114661785600, 2751882854400, 66045188505300];; for n in [11..30] do a[n]:=23*Sum([1..9], j-> a[n-j]) -276*a[n-10]; od; Concatenation([1], a); # G. C. Greubel, Sep 26 2019
CROSSREFS
Sequence in context: A164638 A164963 A165368 * A166419 A166612 A167078
KEYWORD
nonn
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved