|
|
A164610
|
|
Number of reduced words of length n in Coxeter group on 13 generators S_i with relations (S_i)^2 = (S_i S_j)^7 = I.
|
|
1
|
|
|
1, 13, 156, 1872, 22464, 269568, 3234816, 38817714, 465811632, 5589728430, 67076607312, 804917681568, 9658992904704, 115907683567104, 1390889427339126, 16690639822542972, 200287278204994266
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
COMMENTS
|
The initial terms coincide with those of A170732, although the two sequences are eventually different.
Computed with MAGMA using commands similar to those used to compute A154638.
|
|
LINKS
|
|
|
FORMULA
|
G.f.: (t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(66*t^7 - 11*t^6 - 11*t^5 - 11*t^4 - 11*t^3 - 11*t^2 - 11*t + 1).
|
|
MAPLE
|
seq(coeff(series((1+t)*(1-t^7)/(1-12*t+77*t^7-66*t^8), t, n+1), t, n), n = 0..20); # G. C. Greubel, Sep 15 2019
|
|
MATHEMATICA
|
CoefficientList[Series[(1+t)*(1-t^7)/(1-12*t+77*t^7-66*t^8), {t, 0, 20}], t] (* G. C. Greubel, Aug 10 2017 *)
|
|
PROG
|
(PARI) my(t='t+O('t^20)); Vec((1+t)*(1-t^7)/(1-12*t+77*t^7-66*t^8)) \\ G. C. Greubel, Aug 10 2017
(Magma) R<t>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+t)*(1-t^7)/(1-12*t+77*t^7-66*t^8) )); // G. C. Greubel, Sep 15 2019
(Sage)
P.<t> = PowerSeriesRing(ZZ, prec)
return P((1+t)*(1-t^7)/(1-12*t+77*t^7-66*t^8)).list()
(GAP) a:=[13, 156, 1872, 22464, 269568, 3234816, 38817714];; for n in [8..20] do a[n]:=11*(a[n-1] +a[n-2]+a[n-3]+a[n-4]+a[n-5]+a[n-6]) -66*a[n-7]; od; Concatenation([1], a); # G. C. Greubel, Sep 15 2019
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|