|
|
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
(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^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 *)
|
|
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)
P.<t> = PowerSeriesRing(ZZ, prec)
return P((1+t)*(1-t^5)/(1-49*t+1224*t^5-1176*t^6)).list()
(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
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|