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A164618
Number of reduced words of length n in Coxeter group on 14 generators S_i with relations (S_i)^2 = (S_i S_j)^7 = I.
1
1, 14, 182, 2366, 30758, 399854, 5198102, 67575235, 878476872, 11420184048, 148462193880, 1930005936768, 25090043590248, 326170130032656, 4240206014105334, 55122604391319192, 716592897791781192
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.
FORMULA
G.f.: (t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(78*t^7 - 12*t^6 - 12*t^5 - 12*t^4 - 12*t^3 - 12*t^2 - 12*t + 1).
a(n) = -78*a(n-7) + 12*Sum_{k=1..6} a(n-k). - Wesley Ivan Hurt, May 11 2021
MAPLE
seq(coeff(series((1+t)*(1-t^7)/(1-13*t+90*t^7-78*t^8), t, n+1), t, n), n = 0..20); # G. C. Greubel, Sep 15 2019
MATHEMATICA
CoefficientList[Series[(1+t)*(1-t^7)/(1-13*t+90*t^7-78*t^8), {t, 0, 20}], t] (* G. C. Greubel, Aug 10 2017 *)
coxG[{7, 78, -12}] (* The coxG program is at A169452 *) (* G. C. Greubel, Sep 15 2019 *)
PROG
(PARI) my(t='t+O('t^20)); Vec((1+t)*(1-t^7)/(1-13*t+90*t^7-78*t^8)) \\ G. C. Greubel, Aug 10 2017
(Magma) R<t>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+t)*(1-t^7)/(1-13*t+90*t^7-78*t^8) )); // G. C. Greubel, Sep 15 2019
(Sage)
def A164618_list(prec):
P.<t> = PowerSeriesRing(ZZ, prec)
return P((1+t)*(1-t^7)/(1-13*t+90*t^7-78*t^8)).list()
A164618_list(20) # G. C. Greubel, Sep 15 2019
(GAP) a:=[14, 182, 2366, 30758, 399854, 5198102, 67575235];; for n in [8..20] do a[n]:=12*(a[n-1] +a[n-2]+a[n-3]+a[n-4]+a[n-5]+a[n-6]) -78*a[n-6]; od; Concatenation([1], a); # G. C. Greubel, Sep 15 2019
CROSSREFS
Sequence in context: A163090 A163439 A163959 * A164835 A165270 A165874
KEYWORD
nonn
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved