|
|
A163957
|
|
Number of reduced words of length n in Coxeter group on 12 generators S_i with relations (S_i)^2 = (S_i S_j)^6 = I.
|
|
1
|
|
|
1, 12, 132, 1452, 15972, 175692, 1932546, 21257280, 233822160, 2571956640, 28290564720, 311185670400, 3422926421970, 37650915208500, 414146038003500, 4555452101075700, 50108275682741100, 551172361422635700
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
COMMENTS
|
The initial terms coincide with those of A003954, 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)/(55*t^6 - 10*t^5 - 10*t^4 - 10*t^3 - 10*t^2 - 10*t + 1).
|
|
MAPLE
|
seq(coeff(series((1+t)*(1-t^6)/(1-11*t+65*t^6-55*t^7), t, n+1), t, n), n = 0 .. 30); # G. C. Greubel, Aug 10 2019
|
|
MATHEMATICA
|
CoefficientList[Series[(1+t)*(1-t^6)/(1-11*t+65*t^6-55*t^7), {t, 0, 30}], t] (* G. C. Greubel, Aug 13 2017 *)
|
|
PROG
|
(PARI) my(t='t+O('t^30)); Vec((1+t)*(1-t^6)/(1-11*t+65*t^6-55*t^7)) \\ G. C. Greubel, Aug 13 2017
(Magma) R<t>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1+t)*(1-t^6)/(1-11*t+65*t^6-55*t^7) )); // G. C. Greubel, Aug 10 2019
(Sage)
P.<t> = PowerSeriesRing(ZZ, prec)
return P((1+t)*(1-t^6)/(1-11*t+65*t^6-55*t^7)).list()
(GAP) a:=[12, 132, 1452, 15972, 175692, 1932546];; for n in [7..30] do a[n]:=10*(a[n-1] +a[n-2]+a[n-3]+a[n-4]+a[n-5]) -55*a[n-6]; od; Concatenation([1], a); # G. C. Greubel, Aug 10 2019
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|