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A164017
Number of reduced words of length n in Coxeter group on 27 generators S_i with relations (S_i)^2 = (S_i S_j)^6 = I.
1
1, 27, 702, 18252, 474552, 12338352, 320796801, 8340707700, 216858163275, 5638306085100, 146595798051300, 3811486585140000, 99098542944724050, 2576559301574090625, 66990468651299212500, 1741750282005552804375
OFFSET
0,2
COMMENTS
The initial terms coincide with those of A170746, 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)/(325*t^6 - 25*t^5 - 25*t^4 - 25*t^3 - 25*t^2 - 25*t + 1).
a(n) = -325*a(n-6) + 25*Sum_{k=1..5} a(n-k). - Wesley Ivan Hurt, May 11 2021
MAPLE
seq(coeff(series((1+t)*(1-t^6)/(1-26*t+350*t^6-325*t^7), t, n+1), t, n), n = 0 .. 30); # G. C. Greubel, Aug 13 2019
MATHEMATICA
coxG[{6, 325, -25}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Jun 26 2017 *)
CoefficientList[Series[(1+t)*(1-t^6)/(1-26*t+350*t^6-325*t^7), {t, 0, 30}], t] (* G. C. Greubel, Sep 07 2017 *)
PROG
(PARI) my(t='t+O('t^30)); Vec((1+t)*(1-t^6)/(1-26*t+350*t^6-325*t^7)) \\ G. C. Greubel, Sep 07 2017
(Magma) R<t>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1+t)*(1-t^6)/(1-26*t+350*t^6-325*t^7) )); // G. C. Greubel, Aug 13 2019
(Sage)
def A164017_list(prec):
P.<t> = PowerSeriesRing(ZZ, prec)
return P((1+t)*(1-t^6)/(1-26*t+350*t^6-325*t^7)).list()
A164017_list(30) # G. C. Greubel, Aug 13 2019
(GAP) a:=[27, 702, 18252, 474552, 12338352, 320796801];; for n in [7..30] do a[n]:=25*(a[n-1] +a[n-2]+a[n-3]+a[n-4]+a[n-5]) -325*a[n-6]; od; Concatenation([1], a); # G. C. Greubel, Aug 13 2019
CROSSREFS
Sequence in context: A162827 A163179 A163527 * A164644 A164969 A165445
KEYWORD
nonn
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved