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A164350
Number of reduced words of length n in Coxeter group on 49 generators S_i with relations (S_i)^2 = (S_i S_j)^6 = I.
1
1, 49, 2352, 112896, 5419008, 260112384, 12485393256, 599298819840, 28766340643992, 1380784220911872, 66277636363782144, 3181326245942132736, 152703645428292064680, 7329774290465429385408, 351829132817899422588504, 16887796785286144959221568
OFFSET
0,2
COMMENTS
The initial terms coincide with those of A170768, although the two sequences are eventually different.
Computed with MAGMA using commands similar to those used to compute A154638.
LINKS
FORMULA
G.f.: (t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(1128*t^6 - 47*t^5 - 47*t^4 - 47*t^3 - 47*t^2 - 47*t + 1).
a(n) = -1128*a(n-6) + 47*Sum_{k=1..5} a(n-k). - Wesley Ivan Hurt, May 11 2021
MAPLE
seq(coeff(series((1+t)*(1-t^6)/(1-48*t+1175*t^6-1128*t^7), t, n+1), t, n), n = 0..20); # G. C. Greubel, Aug 24 2019
MATHEMATICA
CoefficientList[Series[(1+t)*(1-t^6)/(1-48*t+1175*t^6-1128*t^7), {t, 0, 20}], t] (* G. C. Greubel, Sep 15 2017 *)
coxG[{6, 1128, -47}] (* The coxG program is at A169452 *) (* G. C. Greubel, Aug 24 2019 *)
PROG
(PARI) my(t='t+O('t^20)); Vec((1+t)*(1-t^6)/(1-48*t+1175*t^6-1128*t^7)) \\ G. C. Greubel, Sep 15 2017
(Magma) R<t>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+t)*(1-t^6)/(1-48*t+1175*t^6-1128*t^7) )); // G. C. Greubel, Aug 24 2019
(Sage)
def A164350_list(prec):
P.<t> = PowerSeriesRing(ZZ, prec)
return P((1+t)*(1-t^6)/(1-48*t+1175*t^6-1128*t^7)).list()
A164350_list(20) # G. C. Greubel, Aug 24 2019
(GAP) a:=[49, 2352, 112896, 5419008, 260112384, 12485393256];; for n in [7..20] do a[n]:=47*(a[n-1] +a[n-2]+a[n-3]+a[n-4]+a[n-5]) -1128*a[n-6]; od; Concatenation([1], a); # G. C. Greubel, Aug 24 2019
CROSSREFS
Sequence in context: A162914 A163287 A163835 * A164694 A165181 A165709
KEYWORD
nonn
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved