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A163968
Number of reduced words of length n in Coxeter group on 19 generators S_i with relations (S_i)^2 = (S_i S_j)^6 = I.
1
1, 19, 342, 6156, 110808, 1994544, 35901621, 646226100, 11632014567, 209375268012, 3768736928724, 67836942598176, 1221059168656830, 21978960670333953, 395619413496128064, 7121115628832971863, 128179472668131616290, 2307219552362877498072, 41529754741525340825124
OFFSET
0,2
COMMENTS
The initial terms coincide with those of A170738, 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)/(153*t^6 - 17*t^5 - 17*t^4 - 17*t^3 - 17*t^2 - 17*t + 1).
a(n) = -153*a(n-6) + 17*Sum_{k=1..5} a(n-k). - Wesley Ivan Hurt, May 11 2021
MAPLE
seq(coeff(series((1+t)*(1-t^6)/(1-18*t+170*t^6-153*t^7), t, n+1), t, n), n = 0 .. 30); # G. C. Greubel, Aug 11 2019
MATHEMATICA
CoefficientList[Series[(1+t)*(1-t^6)/(1-18*t+170*t^6-153*t^7), {t, 0, 30}], t] (* G. C. Greubel, Aug 23 2017 *)
coxG[{6, 153, -17}] (* 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)/(1-18*t+170*t^6-153*t^7)) \\ G. C. Greubel, Aug 23 2017
(Magma) R<t>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1+t)*(1-t^6)/(1-18*t+170*t^6-153*t^7) )); // G. C. Greubel, Aug 11 2019
(Sage)
def A163968_list(prec):
P.<t> = PowerSeriesRing(ZZ, prec)
return P((1+t)*(1-t^6)/(1-18*t+170*t^6-153*t^7)).list()
A163968_list(30) # G. C. Greubel, Aug 11 2019
(GAP) a:=[19, 342, 6156, 110808, 1994544, 35901621];; for n in [7..30] do a[n]:=17*(a[n-1] +a[n-2]+a[n-3]+a[n-4]+a[n-5]) -153*a[n-6]; od; Concatenation([1], a); # G. C. Greubel, Aug 11 2019
CROSSREFS
Sequence in context: A049664 A163110 A163453 * A164631 A164909 A165341
KEYWORD
nonn,easy
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved