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A165874
Number of reduced words of length n in Coxeter group on 14 generators S_i with relations (S_i)^2 = (S_i S_j)^10 = I.
1
1, 14, 182, 2366, 30758, 399854, 5198102, 67575326, 878479238, 11420230094, 148462991131, 1930018883520, 25090245470472, 326173190917392, 4240251479342424, 55123269197863776, 716602499135588520
OFFSET
0,2
COMMENTS
The initial terms coincide with those of A170733, 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 (12,12,12,12,12,12,12,12,12,-78).
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)/(78*t^10 - 12*t^9 - 12*t^8 - 12*t^7 - 12*t^6 - 12*t^5 - 12*t^4 - 12*t^3 - 12*t^2 - 12*t + 1).
MAPLE
seq(coeff(series((1+t)*(1-t^10)/(1-13*t+90*t^10-78*t^11), t, n+1), t, n), n = 0..20); # G. C. Greubel, Sep 23 2019
MATHEMATICA
CoefficientList[Series[(1+t)*(1-t^10)/(1-13*t+90*t^10-78*t^11), {t, 0, 25}], t] (* G. C. Greubel, Apr 17 2016 *)
coxG[{10, 78, -12}] (* The coxG program is at A169452 *) (* G. C. Greubel, Sep 23 2019 *)
PROG
(PARI) my(t='t+O('t^20)); Vec((1+t)*(1-t^10)/(1-13*t+90*t^10-78*t^11)) \\ G. C. Greubel, Sep 23 2019
(Magma) R<t>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+t)*(1-t^10)/(1-13*t+90*t^10-78*t^11) )); // G. C. Greubel, Sep 23 2019
(Sage)
def A165874_list(prec):
P.<t> = PowerSeriesRing(ZZ, prec)
return P((1+t)*(1-t^10)/(1-13*t+90*t^10-78*t^11)).list()
A165874_list(20) # G. C. Greubel, Sep 23 2019
(GAP) a:=[14, 182, 2366, 30758, 399854, 5198102, 67575326, 878479238, 11420230094, 148462991131];; for n in [11..20] do a[n]:=12*Sum([1..9], j-> a[n-j]) -78*a[n-10]; od; Concatenation([1], a); # G. C. Greubel, Sep 23 2019
CROSSREFS
Sequence in context: A164618 A164835 A165270 * A166379 A166568 A166969
KEYWORD
nonn
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved