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A163924
Number of reduced words of length n in Coxeter group on 8 generators S_i with relations (S_i)^2 = (S_i S_j)^6 = I.
1
1, 8, 56, 392, 2744, 19208, 134428, 940800, 6584256, 46080384, 322496832, 2257016832, 15795891636, 110548662840, 773682621768, 5414672451384, 37894967433288, 265210605012024, 1856095143363468, 12990012903371952
OFFSET
0,2
COMMENTS
The initial terms coincide with those of A003950, although the two sequences are eventually different.
Computed with MAGMA using commands similar to those used to compute A154638.
FORMULA
G.f.: (t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(21*t^6 - 6*t^5 - 6*t^4 - 6*t^3 - 6*t^2 - 6*t + 1).
a(n) = -21*a(n-6) + 6*Sum_{k=1..5} a(n-k). - Wesley Ivan Hurt, May 11 2021
MAPLE
seq(coeff(series((1+t)*(1-t^6)/(1-7*t+27*t^6-21*t^7), t, n+1), t, n), n = 0 .. 30); # G. C. Greubel, Aug 10 2019
MATHEMATICA
coxG[{6, 21, -6}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Jan 24 2016 *)
CoefficientList[Series[(1+t)*(1-t^6)/(1-7*t+27*t^6-21*t^7), {t, 0, 30}], t] (* G. C. Greubel, Aug 08 2017 *)
PROG
(PARI) my(t='t+O('t^30)); Vec((1+t)*(1-t^6)/(1-7*t+27*t^6-21*t^7)) \\ G. C. Greubel, Aug 08 2017
(Magma) R<t>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1+t)*(1-t^6)/(1-7*t+27*t^6-21*t^7) )); // G. C. Greubel, Aug 10 2019
(Sage)
def A163924_list(prec):
P.<t> = PowerSeriesRing(ZZ, prec)
return P((1+t)*(1-t^6)/(1-7*t+27*t^6-21*t^7)).list()
A163924_list(30) # G. C. Greubel, Aug 10 2019
(GAP) a:=[8, 56, 392, 2744, 19208, 134428];; for n in [7..30] do a[n]:=6*(a[n-1] +a[n-2]+a[n-3]+a[n-4]+a[n-5]) -21*a[n-6]; od; Concatenation([1], a); # G. C. Greubel, Aug 10 2019
CROSSREFS
Sequence in context: A063812 A234274 A163347 * A164373 A164769 A165215
KEYWORD
nonn
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved