login
A164070
Number of reduced words of length n in Coxeter group on 37 generators S_i with relations (S_i)^2 = (S_i S_j)^6 = I.
1
1, 37, 1332, 47952, 1726272, 62145792, 2237247846, 80540898480, 2899471482810, 104380942332240, 3757712806199520, 135277620783782400, 4869992899598197770, 175319692235303773500, 6311507043063165819750
OFFSET
0,2
COMMENTS
The initial terms coincide with those of A170756, 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)/(630*t^6 - 35*t^5 - 35*t^4 - 35*t^3 - 35*t^2 - 35*t + 1).
a(n) = -630*a(n-6) + 35*Sum_{k=1..5} a(n-k). - Wesley Ivan Hurt, May 05 2021
MAPLE
seq(coeff(series((1+t)*(1-t^6)/(1-36*t+665*t^6-630*t^7), t, n+1), t, n), n = 0 .. 30); # G. C. Greubel, Aug 16 2019
MATHEMATICA
CoefficientList[Series[(1+t)*(1-t^6)/(1-36*t+665*t^6-630*t^7), {t, 0, 30}], t] (* G. C. Greubel, Sep 09 2017 *)
coxG[{6, 630, -35}] (* The coxG program is at A169452 *) (* G. C. Greubel, Aug 16 2019 *)
PROG
(PARI) my(t='t+O('t^30)); Vec((1+t)*(1-t^6)/(1-36*t+665*t^6-630*t^7)) \\ G. C. Greubel, Sep 09 2017
(Magma) R<t>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1+t)*(1-t^6)/(1-36*t+665*t^6-630*t^7) )); // G. C. Greubel, Aug 16 2019
(Sage)
def A164070_list(prec):
P.<t> = PowerSeriesRing(ZZ, prec)
return P((1+t)*(1-t^6)/(1-36*t+665*t^6-630*t^7)).list()
A164070_list(30) # G. C. Greubel, Aug 16 2019
(GAP) a:=[37, 1332, 47952, 1726272, 62145792, 2237247846];; for n in [7..30] do a[n]:=35*(a[n-1] +a[n-2]+a[n-3]+a[n-4]+a[n-5]) -630*a[n-6]; od; Concatenation([1], a); # G. C. Greubel, Aug 16 2019
CROSSREFS
Sequence in context: A162851 A163220 A163645 * A164673 A165169 A165654
KEYWORD
nonn
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved