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A164351 Number of reduced words of length n in Coxeter group on 50 generators S_i with relations (S_i)^2 = (S_i S_j)^6 = I. 1
1, 50, 2450, 120050, 5882450, 288240050, 14123761225, 692064240000, 33911144820000, 1661645952120000, 81420644594940000, 3989611239264000000, 195490933775422559400, 9579054924518618851200, 469373650608038610268800 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
The initial terms coincide with those of A170769, 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)/(1176*t^6 - 48*t^5 - 48*t^4 - 48*t^3 - 48*t^2 - 48*t + 1).
a(n) = -1176*a(n-6) + 48*Sum_{k=1..5} a(n-k). - Wesley Ivan Hurt, May 11 2021
MAPLE
seq(coeff(series((1+t)*(1-t^6)/(1-49*t+1224*t^6-1176*t^7), t, n+1), t, n), n = 0 .. 20); # G. C. Greubel, Aug 24 2019
MATHEMATICA
coxG[{6, 1176, -48}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Feb 18 2015 *)
CoefficientList[Series[(1+t)*(1-t^6)/(1-49*t+1224*t^6-1176*t^7), {t, 0, 20}], t] (* G. C. Greubel, Sep 15 2017 *)
PROG
(PARI) my(t='t+O('t^20)); Vec((1+t)*(1-t^6)/(1-49*t+1224*t^6-1176*t^7)) \\ G. C. Greubel, Sep 15 2017
(Magma) R<t>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+t)*(1-t^6)/(1-49*t+1224*t^6-1176*t^7) )); // G. C. Greubel, Aug 24 2019
(Sage)
def A164351_list(prec):
P.<t> = PowerSeriesRing(ZZ, prec)
return P((1+t)*(1-t^6)/(1-49*t+1224*t^6-1176*t^7)).list()
A164351_list(20) # G. C. Greubel, Aug 24 2019
(GAP) a:=[50, 2450, 120050, 5882450, 288240050, 14123761225];; for n in [7..20] do a[n]:=48*(a[n-1] +a[n-2]+a[n-3]+a[n-4]+a[n-5]) -1176*a[n-6]; od; Concatenation([1], a); # G. C. Greubel, Aug 24 2019
CROSSREFS
Sequence in context: A162919 A163290 A163837 * A164695 A165182 A165726
KEYWORD
nonn
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved

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Last modified March 28 07:48 EDT 2024. Contains 371235 sequences. (Running on oeis4.)