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A163992
Number of reduced words of length n in Coxeter group on 24 generators S_i with relations (S_i)^2 = (S_i S_j)^6 = I.
1
1, 24, 552, 12696, 292008, 6716184, 154471956, 3552848640, 81715372992, 1879450227072, 43227278132544, 994225623975936, 22867148570853180, 525943479177652008, 12096678448229129304, 278223108134446896168
OFFSET
0,2
COMMENTS
The initial terms coincide with those of A170743, 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)/(253*t^6 - 22*t^5 - 22*t^4 - 22*t^3 - 22*t^2 - 22*t + 1).
a(n) = -253*a(n-6) + 22*Sum_{k=1..5} a(n-k). - Wesley Ivan Hurt, May 11 2021
MAPLE
seq(coeff(series((1+t)*(1-t^6)/(1-23*t+275*t^6-253*t^7), t, n+1), t, n), n = 0 .. 30); # G. C. Greubel, Aug 11 2019
MATHEMATICA
CoefficientList[Series[(1+t)*(1-t^6)/(1-23*t+275*t^6-253*t^7), {t, 0, 30}], t] (* G. C. Greubel, Aug 24 2017 *)
coxG[{6, 253, -22}] (* The coxG program is at A169452 *) (* G. C. Greubel, Aug 11 2019 *)
PROG
(PARI) my(t='t+O('t^30)); Vec((1+t)*(1-t^6)/(1-23*t+275*t^6-253*t^7)) \\ G. C. Greubel, Aug 24 2017
(Magma) R<t>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1+t)*(1-t^6)/(1-23*t+275*t^6-253*t^7) )); // G. C. Greubel, Aug 11 2019
(Sage)
def A163992_list(prec):
P.<t> = PowerSeriesRing(ZZ, prec)
return P((1+t)*(1-t^6)/(1-23*t+275*t^6-253*t^7)).list()
A163992_list(30) # G. C. Greubel, Aug 11 2019
(GAP) a:=[24, 552, 12696, 292008, 6716184, 154471956];; for n in [7..30] do a[n]:=22*(a[n-1] +a[n-2]+a[n-3]+a[n-4]+a[n-5]) -253*a[n-6]; od; Concatenation([1], a); # G. C. Greubel, Aug 11 2019
CROSSREFS
Sequence in context: A342888 A163174 A163519 * A164637 A164959 A165366
KEYWORD
nonn
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved