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A163922
Number of reduced words of length n in Coxeter group on 6 generators S_i with relations (S_i)^2 = (S_i S_j)^6 = I.
1
1, 6, 30, 150, 750, 3750, 18735, 93600, 467640, 2336400, 11673000, 58320000, 291375210, 1455753000, 7273154040, 36337737000, 181548627000, 907043385000, 4531720872060, 22641137570400, 113118421225440, 565156109349600
OFFSET
0,2
COMMENTS
The initial terms coincide with those of A003948, 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)/(10*t^6 - 4*t^5 - 4*t^4 - 4*t^3 - 4*t^2 - 4*t + 1).
a(n) = -10*a(n-6) + 4*Sum_{k=1..5} a(n-k). - Wesley Ivan Hurt, May 11 2021
MAPLE
seq(coeff(series((1+t)*(1-t^6)/(1-5*t+14*t^6-10*t^7), t, n+1), t, n), n = 0 .. 30); # G. C. Greubel, Aug 10 2019
MATHEMATICA
coxG[{6, 10, -4, 30}] (* The coxG program is at A169452 *) (* Harvey P. Dale, May 13 2017 *)
CoefficientList[Series[(1+t)*(1-t^6)/(1-5*t+14*t^6-10*t^7), {t, 0, 30}], t] (* G. C. Greubel, Aug 07 2017 *)
PROG
(PARI) my(t='t+O('t^30)); Vec((1+t)*(1-t^6)/(1-5*t+14*t^6-10*t^7)) \\ G. C. Greubel, Aug 07 2017
(Magma) R<t>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1+t)*(1-t^6)/(1-5*t+14*t^6-10*t^7) )); // G. C. Greubel, Aug 10 2019
(Sage)
def A163922_list(prec):
P.<t> = PowerSeriesRing(ZZ, prec)
return P((1+t)*(1-t^6)/(1-5*t+14*t^6-10*t^7)).list()
A163922_list(30) # G. C. Greubel, Aug 10 2019
(GAP) a:=[6, 30, 150, 750, 3750, 18735];; for n in [7..30] do a[n]:=4*(a[n-1] +a[n-2]+a[n-3]+a[n-4]+a[n-5]) -10*a[n-6]; od; Concatenation([1], a); # G. C. Greubel, Aug 10 2019
CROSSREFS
Sequence in context: A006819 A163317 A342807 * A164365 A164741 A165213
KEYWORD
nonn
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved