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A164069
Number of reduced words of length n in Coxeter group on 36 generators S_i with relations (S_i)^2 = (S_i S_j)^6 = I.
1
1, 36, 1260, 44100, 1543500, 54022500, 1890786870, 66177518400, 2316212372880, 81067406061600, 2837358267534000, 99307506301920000, 3475761563405646270, 121651614218556733500, 4257805080127526578980, 149023128191211379381500
OFFSET
0,2
COMMENTS
The initial terms coincide with those of A170755, 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)/(595*t^6 - 34*t^5 - 34*t^4 - 34*t^3 - 34*t^2 - 34*t + 1).
a(n) = -595*a(n-6) + 34*Sum_{k=1..5} a(n-k). - Wesley Ivan Hurt, May 11 2021
MAPLE
seq(coeff(series((1+t)*(1-t^6)/(1-35*t+629*t^6-595*t^7), t, n+1), t, n), n = 0 .. 30); # G. C. Greubel, Aug 13 2019
MATHEMATICA
CoefficientList[Series[(1+t)*(1-t^6)/(1-35*t+629*t^6-595*t^7), {t, 0, 30}], t] (* G. C. Greubel, Sep 09 2017 *)
coxG[{6, 595, -34}] (* The coxG program is at A169452 *) (* G. C. Greubel, Aug 13 2019 *)
PROG
(PARI) t='t+O('t^50); Vec((1+t)*(1-t^6)/(1-35*t+629*t^6-595*t^7)) \\ G. C. Greubel, Sep 09 2017
(Magma) R<t>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1+t)*(1-t^6)/(1-35*t+629*t^6-595*t^7) )); // G. C. Greubel, Aug 13 2019
(Sage)
def A164069_list(prec):
P.<t> = PowerSeriesRing(ZZ, prec)
return P((1+t)*(1-t^6)/(1-35*t+629*t^6-595*t^7)).list()
A164069_list(30) # G. C. Greubel, Aug 13 2019
(GAP) a:=[36, 1260, 44100, 1543500, 54022500, 1890786870];; for n in [7..30] do a[n]:=34*(a[n-1] +a[n-2]+a[n-3]+a[n-4]+a[n-5]) -595*a[n-6]; od; Concatenation([1], a); # G. C. Greubel, Aug 13 2019
CROSSREFS
Sequence in context: A162850 A163219 A163601 * A164672 A165168 A165651
KEYWORD
nonn
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved