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A163953
Number of reduced words of length n in Coxeter group on 9 generators S_i with relations (S_i)^2 = (S_i S_j)^6 = I.
1
1, 9, 72, 576, 4608, 36864, 294876, 2358720, 18867492, 150921792, 1207229184, 9656672256, 77244089580, 617878417968, 4942433025684, 39534710232528, 316239654648960, 2529613056079872, 20234471292326844, 161856307428494112
OFFSET
0,2
COMMENTS
The initial terms coincide with those of A003951, 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)/(28*t^6 - 7*t^5 - 7*t^4 - 7*t^3 - 7*t^2 - 7*t + 1).
a(n) = -28*a(n-6) + 7*Sum_{k=1..5} a(n-k). - Wesley Ivan Hurt, May 11 2021
MAPLE
seq(coeff(series((1+t)*(1-t^6)/(1-8*t+35*t^6-28*t^7), t, n+1), t, n), n = 0 .. 30); # G. C. Greubel, Aug 10 2019
MATHEMATICA
CoefficientList[Series[(1+t)*(1-t^6)/(1-8*t+35*t^6-28*t^7), {t, 0, 30}], t] (* G. C. Greubel, Aug 13 2017 *)
coxG[{6, 28, -7}] (* The coxG program is at A169452 *) (* G. C. Greubel, Aug 10 2019 *)
PROG
(PARI) my(t='t+O('t^30)); Vec((1+t)*(1-t^6)/(1-8*t+35*t^6-28*t^7)) \\ G. C. Greubel, Aug 13 2017
(Magma) R<t>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1+t)*(1-t^6)/(1-8*t+35*t^6-28*t^7) )); // G. C. Greubel, Aug 10 2019
(Sage)
def A163953_list(prec):
P.<t> = PowerSeriesRing(ZZ, prec)
return P((1+t)*(1-t^6)/(1-8*t+35*t^6-28*t^7)).list()
A163953_list(30) # G. C. Greubel, Aug 10 2019
(GAP) a:=[9, 72, 576, 4608, 36864, 294876];; for n in [7..30] do a[n]:=7*(a[n-1]+a[n-2]+a[n-3]+a[n-4]+a[n-5]) -28*a[n-6]; od; Concatenation([1], a); # G. C. Greubel, Aug 10 2019
CROSSREFS
Sequence in context: A129328 A162960 A163391 * A164375 A164777 A165216
KEYWORD
nonn
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved