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A165880
Number of reduced words of length n in Coxeter group on 18 generators S_i with relations (S_i)^2 = (S_i S_j)^10 = I.
1
1, 18, 306, 5202, 88434, 1503378, 25557426, 434476242, 7386096114, 125563633938, 2134581776793, 36287890202880, 616894133404896, 10487200267134144, 178282404528545952, 3030800876768794752, 51523614901389241440
OFFSET
0,2
COMMENTS
The initial terms coincide with those of A170737, 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 (16,16,16,16,16,16,16,16,16,-136).
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)/(136*t^10 - 16*t^9 - 16*t^8 - 16*t^7 - 16*t^6 - 16*t^5 - 16*t^4 - 16*t^3 - 16*t^2 - 16*t + 1).
MAPLE
seq(coeff(series((1+t)*(1-t^10)/(1-17*t+152*t^10-136*t^11), t, n+1), t, n), n = 0..20); # G. C. Greubel, Sep 24 2019
MATHEMATICA
CoefficientList[Series[(1+t)*(1-t^10)/(1-17*t+152*t^10-136*t^11), {t, 0, 20}], t] (* G. C. Greubel, Apr 17 2016 *)
coxG[{10, 136, -16}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Nov 04 2017 *)
PROG
(PARI) my(t='t+O('t^20)); Vec((1+t)*(1-t^10)/(1-17*t+152*t^10-136*t^11)) \\ G. C. Greubel, Sep 24 2019
(Magma) R<t>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+t)*(1-t^10)/(1-17*t+152*t^10-136*t^11) )); // G. C. Greubel, Sep 24 2019
(Sage)
def A165880_list(prec):
P.<t> = PowerSeriesRing(ZZ, prec)
return P((1+t)*(1-t^10)/(1-17*t+152*t^10-136*t^11)).list()
A165880_list(20) # G. C. Greubel, Sep 24 2019
(GAP) a:=[18, 306, 5202, 88434, 1503378, 25557426, 434476242, 7386096114, 125563633938, 2134581776793];; for n in [11..20] do a[n]:=16*Sum([1..9], j-> a[n-j]) -136*a[n-10]; od; Concatenation([1], a); # G. C. Greubel, Sep 24 2019
CROSSREFS
Sequence in context: A164630 A164892 A165329 * A166412 A166599 A167048
KEYWORD
nonn
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved