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A164348
Number of reduced words of length n in Coxeter group on 48 generators S_i with relations (S_i)^2 = (S_i S_j)^6 = I.
2
1, 48, 2256, 106032, 4983504, 234224688, 11008559208, 517402229760, 24317902308096, 1142941291421184, 53718235195007232, 2524756795581284352, 118663557238871024856, 5577186619014877732560, 262127744246735162576688
OFFSET
0,2
COMMENTS
The initial terms coincide with those of A170767, although the two sequences are eventually different.
Computed with MAGMA using commands similar to those used to compute A154638.
LINKS
FORMULA
G.f.: (t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(1081*t^6 - 46*t^5 - 46*t^4 - 46*t^3 - 46*t^2 - 46*t + 1).
a(n) = -1081*a(n-6) + 46*Sum_{k=1..5} a(n-k). - Wesley Ivan Hurt, May 07 2021
MAPLE
seq(coeff(series((1+t)*(1-t^6)/(1-47*t+1127*t^6-1081*t^7), t, n+1), t, n), n = 0..20); # G. C. Greubel, Aug 24 2019
MATHEMATICA
CoefficientList[Series[(1+t)*(1-t^6)/(1-47*t+1127*t^6-1081*t^7), {t, 0, 20}], t] (* G. C. Greubel, Sep 15 2017 *)
coxG[{6, 1081, -46}] (* The coxG program is at A169452 *) (* G. C. Greubel, Aug 24 2019 *)
PROG
(PARI) my(t='t+O('t^20)); Vec((1+t)*(1-t^6)/(1-47*t+1127*t^6-1081*t^7)) \\ G. C. Greubel, Sep 15 2017
(Magma) R<t>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+t)*(1-t^6)/(1-47*t+1127*t^6-1081*t^7) )); // G. C. Greubel, Aug 24 2019
(Sage)
def A164348_list(prec):
P.<t> = PowerSeriesRing(ZZ, prec)
return P((1+t)*(1-t^6)/(1-47*t+1127*t^6-1081*t^7)).list()
A164348_list(20) # G. C. Greubel, Aug 24 2019
(GAP) a:=[48, 2256, 106032, 4983504, 234224688, 11008559208];; for n in [7..20] do a[n]:=46*(a[n-1] +a[n-2]+a[n-3]+a[n-4]+a[n-5]) -1081*a[n-6]; od; Concatenation([1], a); # G. C. Greubel, Aug 24 2019
CROSSREFS
Sequence in context: A156093 A163266 A163829 * A164693 A165180 A165708
KEYWORD
nonn
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved