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A163923
Number of reduced words of length n in Coxeter group on 7 generators S_i with relations (S_i)^2 = (S_i S_j)^6 = I.
1
1, 7, 42, 252, 1512, 9072, 54411, 326340, 1957305, 11739420, 70410060, 422301600, 2532857460, 15191434125, 91114353750, 546480693675, 3277652052150, 19658522431800, 117906811965600, 707175035973000, 4241455800274875
OFFSET
0,2
COMMENTS
The initial terms coincide with those of A003949, 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)/(15*t^6 - 5*t^5 - 5*t^4 - 5*t^3 - 5*t^2 - 5*t + 1).
a(n) = 5*a(n-1)+5*a(n-2)+5*a(n-3)+5*a(n-4)+5*a(n-5)-15*a(n-6). - Wesley Ivan Hurt, Apr 23 2021
MAPLE
seq(coeff(series((1+t)*(1-t^6)/(1-6*t+20*t^6-15*t^7), t, n+1), t, n), n = 0 .. 30); # G. C. Greubel, Aug 10 2019
MATHEMATICA
coxG[{6, 15, -5}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Aug 18 2015 *)
CoefficientList[Series[(1+t)*(1-t^6)/(1-6*t+20*t^6-15*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)/(1-6*t+20*t^6-15*t^7)) \\ G. C. Greubel, Aug 08 2017
(Magma) R<t>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1+t)*(1-t^6)/(1-6*t+20*t^6-15*t^7) )); // G. C. Greubel, Aug 10 2019
(Sage)
def A163923_list(prec):
P.<t> = PowerSeriesRing(ZZ, prec)
return P((1+t)*(1-t^6)/(1-6*t+20*t^6-15*t^7)).list()
A163923_list(30) # G. C. Greubel, Aug 10 2019
(GAP) a:=[7, 42, 252, 1512, 9072, 54411];; for n in [7..30] do a[n]:=5*(a[n-1] +a[n-2]+a[n-3]+a[n-4]+a[n-5]) -15*a[n-6]; od; Concatenation([1], a); # G. C. Greubel, Aug 10 2019
CROSSREFS
Sequence in context: A162941 A094168 A163345 * A164369 A164742 A165214
KEYWORD
nonn
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved