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A163967
Number of reduced words of length n in Coxeter group on 18 generators S_i with relations (S_i)^2 = (S_i S_j)^6 = I.
1
1, 18, 306, 5202, 88434, 1503378, 25557273, 434471040, 7385963616, 125560632384, 2134518016032, 36286589786112, 616868346117816, 10486699320193920, 178272824864888448, 3030619941978033024, 51520231643134128768
OFFSET
0,2
COMMENTS
The initial terms coincide with those of A170737, 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)/(136*t^6 - 16*t^5 - 16*t^4 - 16*t^3 - 16*t^2 - 16*t + 1).
a(n) = -136*a(n-6) + 16*Sum_{k=1..5} a(n-k). - Wesley Ivan Hurt, May 11 2021
MAPLE
seq(coeff(series((1+t)*(1-t^6)/(1-17*t+152*t^6-136*t^7), t, n+1), t, n), n = 0 .. 30); # G. C. Greubel, Aug 11 2019
MATHEMATICA
CoefficientList[Series[(1+t)*(1-t^6)/(1-17*t+152*t^6-136*t^7), {t, 0, 30}], t] (* G. C. Greubel, Aug 23 2017 *)
coxG[{6, 136, -16}] (* 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)/(1-17*t+152*t^6-136*t^7)) \\ G. C. Greubel, Aug 23 2017
(Magma) R<t>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1+t)*(1-t^6)/(1-17*t+152*t^6-136*t^7) )); // G. C. Greubel, Aug 11 2019
(Sage)
def A163967_list(prec):
P.<t> = PowerSeriesRing(ZZ, prec)
return P((1+t)*(1-t^6)/(1-17*t+152*t^6-136*t^7)).list()
A163967_list(30) # G. C. Greubel, Aug 11 2019
(GAP) a:=[18, 306, 5202, 88434, 1503378, 25557273];; for n in [7..30] do a[n]:=16*(a[n-1] +a[n-2]+a[n-3]+a[n-4]+a[n-5]) -136*a[n-6]; od; Concatenation([1], a); # G. C. Greubel, Aug 11 2019
CROSSREFS
Sequence in context: A342885 A163104 A163452 * A164630 A164892 A165329
KEYWORD
nonn
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved