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A165879
Number of reduced words of length n in Coxeter group on 17 generators S_i with relations (S_i)^2 = (S_i S_j)^10 = I.
1
1, 17, 272, 4352, 69632, 1114112, 17825792, 285212672, 4563402752, 73014444032, 1168231104376, 18691697667840, 299067162650760, 4785074601857280, 76561193620838400, 1224979097791365120, 19599665562389053440
OFFSET
0,2
COMMENTS
The initial terms coincide with those of A170736, 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 (15,15,15,15,15,15,15,15,15,-120).
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)/(120*t^10 - 15*t^9 - 15*t^8 - 15*t^7 - 15*t^6 - 15*t^5 - 15*t^4 - 15*t^3 - 15*t^2 - 15*t + 1).
MAPLE
seq(coeff(series((1+t)*(1-t^10)/(1-16*t+135*t^10-120*t^11), t, n+1), t, n), n = 0 .. 30); # G. C. Greubel, Sep 24 2019
MATHEMATICA
coxG[{10, 120, -15}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Sep 02 2015 *)
CoefficientList[Series[(1+t)*(1-t^10)/(1-16*t+135*t^10-120*t^11), {t, 0, 30}], t] (* G. C. Greubel, Sep 24 2019 *)
PROG
(PARI) my(t='t+O('t^30)); Vec((1+t)*(1-t^10)/(1-16*t+135*t^10-120*t^11)) \\ G. C. Greubel, Sep 24 2019
(Magma) R<t>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1+t)*(1-t^10)/(1-16*t+135*t^10-120*t^11) )); // G. C. Greubel, Sep 24 2019
(Sage)
def A165879_list(prec):
P.<t> = PowerSeriesRing(ZZ, prec)
return P((1+t)*(1-t^10)/(1-16*t+135*t^10-120*t^11)).list()
A165879_list(30) # G. C. Greubel, Sep 24 2019
(GAP) a:=[17, 272, 4352, 69632, 1114112, 17825792, 285212672, 4563402752, 73014444032, 1168231104376];; for n in [11..30] do a[n]:=15*Sum([1..9], j-> a[n-j]) -120*a[n-10]; od; Concatenation([1], a); # G. C. Greubel, Sep 24 2019
CROSSREFS
Sequence in context: A164628 A164868 A165321 * A166411 A166585 A167027
KEYWORD
nonn,easy
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved