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A165873
Number of reduced words of length n in Coxeter group on 13 generators S_i with relations (S_i)^2 = (S_i S_j)^10 = I.
1
1, 13, 156, 1872, 22464, 269568, 3234816, 38817792, 465813504, 5589762048, 67077144498, 804925733040, 9659108785326, 115909305290064, 1390911661874592, 16690939923220992, 200291278847362560
OFFSET
0,2
COMMENTS
The initial terms coincide with those of A170732, 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 (11,11,11,11,11,11,11,11,11,-66).
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)/(66*t^10 - 11*t^9 - 11*t^8 - 11*t^7 - 11*t^6 - 11*t^5 - 11*t^4 - 11*t^3 - 11*t^2 - 11*t + 1).
MAPLE
seq(coeff(series((1+t)*(1-t^10)/(1-12*t+77*t^10-66*t^11), t, n+1), t, n), n = 0 .. 30); # G. C. Greubel, Sep 23 2019
MATHEMATICA
coxG[{10, 66, -11}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Jun 12 2015 *)
CoefficientList[Series[(1+t)*(1-t^10)/(1-12*t+77*t^10-66*t^11), {t, 0, 30}], t] (* G. C. Greubel, Sep 23 2019 *)
PROG
(PARI) my(t='t+O('t^30)); Vec((1+t)*(1-t^10)/(1-12*t+77*t^10-66*t^11)) \\ G. C. Greubel, Sep 23 2019
(Magma) R<t>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1+t)*(1-t^10)/(1-12*t+77*t^10-66*t^11) )); // G. C. Greubel, Sep 23 2019
(Sage)
def A165873_list(prec):
P.<t> = PowerSeriesRing(ZZ, prec)
return P((1+t)*(1-t^10)/(1-12*t+77*t^10-66*t^11)).list()
A165873_list(30) # G. C. Greubel, Sep 23 2019
(GAP) a:=[13, 156, 1872, 22464, 269568, 3234816, 38817792, 465813504, 5589762048, 67077144498];; for n in [7..30] do a[n]:=11*Sum([1..9], j-> a[n-j]) -66*a[n-10]; od; Concatenation([1], a); # G. C. Greubel, Sep 23 2019
CROSSREFS
Sequence in context: A164610 A164815 A165269 * A166377 A166558 A166954
KEYWORD
nonn
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved