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A163837
Number of reduced words of length n in Coxeter group on 50 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I.
1
1, 50, 2450, 120050, 5882450, 288238825, 14123642400, 692055537600, 33910577282400, 1661611227897600, 81418604280421800, 3989494661371228800, 195484407940615651200, 9578695296400885468800, 469354075590339325411200
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.
FORMULA
G.f.: (t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(1176*t^5 - 48*t^4 - 48*t^3 - 48*t^2 - 48*t + 1).
a(n) = 48*a(n-1)+48*a(n-2)+48*a(n-3)+48*a(n-4)-1176*a(n-5). - Wesley Ivan Hurt, May 11 2021
MAPLE
seq(coeff(series((1+t)*(1-t^5)/(1-49*t+1224*t^5-1176*t^6), t, n+1), t, n), n = 0 .. 20); # G. C. Greubel, Aug 09 2019
MATHEMATICA
CoefficientList[Series[(1+t)*(1-t^5)/(1-49*t+1224*t^5-1176*t^6), {t, 0, 20}], t] (* G. C. Greubel, Aug 05 2017 *)
coxG[{5, 1176, -48}] (* The coxG program is at A169452 *) (* G. C. Greubel, Aug 10 2019 *)
PROG
(PARI) my(t='t+O('t^20)); Vec((1+t)*(1-t^5)/(1-49*t+1224*t^5-1176*t^6)) \\ G. C. Greubel, Aug 05 2017 *)
(Magma) R<t>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+t)*(1-t^5)/(1-49*t+1224*t^5-1176*t^6) )); // G. C. Greubel, Aug 09 2019
(Sage)
def A163748_list(prec):
P.<t> = PowerSeriesRing(ZZ, prec)
return P((1+t)*(1-t^5)/(1-49*t+1224*t^5-1176*t^6)).list()
A163748_list(20) # G. C. Greubel, Aug 09 2019
(GAP) a:=[50, 2450, 120050, 5882450, 288238825];; for n in [6..20] do a[n]:=48*(a[n-1]+a[n-2]+a[n-3]+a[n-4]) -1176*a[n-5]; od; Concatenation([1], a); # G. C. Greubel, Aug 09 2019
CROSSREFS
Sequence in context: A156087 A162919 A163290 * A164351 A164695 A165182
KEYWORD
nonn
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved