login
A164050
Number of reduced words of length n in Coxeter group on 34 generators S_i with relations (S_i)^2 = (S_i S_j)^6 = I.
1
1, 34, 1122, 37026, 1221858, 40321314, 1330602801, 43909873920, 1449025228992, 47817812414592, 1577987144990784, 52073553849901056, 1718426553198820080, 56708052368589946368, 1871364939893753424384, 61755017003604231740928
OFFSET
0,2
COMMENTS
The initial terms coincide with those of A170753, 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)/(528*t^6 - 32*t^5 - 32*t^4 - 32*t^3 - 32*t^2 - 32*t + 1).
a(n) = -528*a(n-6) + 32*Sum_{k=1..5} a(n-k). - Wesley Ivan Hurt, May 11 2021
MAPLE
seq(coeff(series((1+t)*(1-t^6)/(1-33*t+560*t^6-528*t^7), t, n+1), t, n), n = 0 .. 30); # G. C. Greubel, Aug 13 2019
MATHEMATICA
CoefficientList[Series[(1+t)*(1-t^6)/(1-33*t+560*t^6-528*t^7), {t, 0, 30}], t] (* G. C. Greubel, Sep 08 2017 *)
LinearRecurrence[{32, 32, 32, 32, 32, -528}, {1, 34, 1122, 37026, 1221858, 40321314, 1330602801}, 21]] (* Vincenzo Librandi, Sep 09 2017 *)
coxG[{6, 528, -2}] (* The coxG program is at A169452 *) (* G. C. Greubel, Aug 13 2019 *)
PROG
(PARI) my(t='t+O('t^30)); Vec((1+t)*(1-t^6)/(1-33*t+560*t^6-528*t^7)) \\ G. C. Greubel, Sep 08 2017
(Magma) R<t>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1+t)*(1-t^6)/(1-33*t+560*t^6-528*t^7) )); // G. C. Greubel, Aug 13 2019
(Sage)
def A164050_list(prec):
P.<t> = PowerSeriesRing(ZZ, prec)
return P((1+t)*(1-t^6)/(1-33*t+560*t^6-528*t^7)).list()
A164050_list(30) # G. C. Greubel, Aug 13 2019
(GAP) a:=[34, 1122, 37026, 1221858, 40321314, 1330602801];; for n in [7..30] do a[n]:=32*(a[n-1] +a[n-2]+a[n-3]+a[n-4]+a[n-5]) -528*a[n-6]; od; Concatenation([1], a); # G. C. Greubel, Aug 13 2019
CROSSREFS
Sequence in context: A162838 A163217 A163593 * A164670 A165166 A165649
KEYWORD
nonn
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved