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A163965
Number of reduced words of length n in Coxeter group on 17 generators S_i with relations (S_i)^2 = (S_i S_j)^6 = I.
1
1, 17, 272, 4352, 69632, 1114112, 17825656, 285208320, 4563298440, 73012220160, 1168186644480, 18690844262400, 299051235428280, 4784783402808000, 76555952624637000, 1224885932940283200, 19598025983313945600
OFFSET
0,2
COMMENTS
The initial terms coincide with those of A170736, 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)/(120*t^6 - 15*t^5 - 15*t^4 - 15*t^3 - 15*t^2 - 15*t + 1).
a(n) = -120*a(n-6) + 15*Sum_{k=1..5} a(n-k). - Wesley Ivan Hurt, May 11 2021
MAPLE
seq(coeff(series((1+t)*(1-t^6)/(1-16*t+135*t^6-120*t^7), t, n+1), t, n), n = 0 .. 30); # G. C. Greubel, Aug 11 2019
MATHEMATICA
CoefficientList[Series[(1+t)*(1-t^6)/(1-16*t+135*t^6-120*t^7), {t, 0, 30}], t] (* G. C. Greubel, Aug 23 2017 *)
coxG[{6, 120, -15}] (* The coxG program is at A169452 *) (* G. C. Greubel, Aug 11 2019 *)
PROG
(PARI) my(t='t+O('t^30)); Vec((1+t)*(1-t^6)/(1-16*t+135*t^6-120*t^7)) \\ G. C. Greubel, Aug 23 2017
(Magma) R<t>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1+t)*(1-t^6)/(1-16*t+135*t^6-120*t^7) )); // G. C. Greubel, Aug 11 2019
(Sage)
def A163965_list(prec):
P.<t> = PowerSeriesRing(ZZ, prec)
return P((1+t)*(1-t^6)/(1-16*t+135*t^6-120*t^7)).list()
A163965_list(30) # G. C. Greubel, Aug 11 2019
(GAP) a:=[17, 272, 4352, 69632, 1114112, 17825656];; for n in [7..30] do a[n]:=15*(a[n-1] +a[n-2]+a[n-3]+a[n-4]+a[n-5]) -120*a[n-6]; od; Concatenation([1], a); # G. C. Greubel, Aug 11 2019
CROSSREFS
Sequence in context: A097830 A163093 A163451 * A164628 A164868 A165321
KEYWORD
nonn
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved