|
|
A165881
|
|
Number of reduced words of length n in Coxeter group on 19 generators S_i with relations (S_i)^2 = (S_i S_j)^10 = I.
|
|
1
|
|
|
1, 19, 342, 6156, 110808, 1994544, 35901792, 646232256, 11632180608, 209379250944, 3768826516821, 67838877299700, 1221099791339367, 21979796243114412, 395636332358163924, 7121453982124831776
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
COMMENTS
|
The initial terms coincide with those of A170738, although the two sequences are eventually different.
Computed with MAGMA using commands similar to those used to compute A154638.
|
|
LINKS
|
Index entries for linear recurrences with constant coefficients, signature (17,17,17,17,17,17,17,17,17,-153).
|
|
FORMULA
|
G.f.: (t^10 + 2*t^9 + 2*t^8 + 2*t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(153*t^10 - 17*t^9 - 17*t^8 - 17*t^7 - 17*t^6 - 17*t^5 - 17*t^4 - 17*t^3 - 17*t^2 - 17*t + 1).
|
|
MAPLE
|
seq(coeff(series((1+t)*(1-t^10)/(1-18*t+170*t^10-153*t^11), t, n+1), t, n), n = 0..20); # G. C. Greubel, Sep 24 2019
|
|
MATHEMATICA
|
CoefficientList[Series[(1+t)*(1-t^10)/(1-18*t+170*t^10-153*t^11), {t, 0, 20}], t] (* G. C. Greubel, Apr 17 2016 *)
|
|
PROG
|
(PARI) my(t='t+O('t^20)); Vec((1+t)*(1-t^10)/(1-18*t+170*t^10-153*t^11)) \\ G. C. Greubel, Sep 24 2019
(Magma) R<t>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+t)*(1-t^10)/(1-18*t+170*t^10-153*t^11) )); // G. C. Greubel, Sep 24 2019
(Sage)
P.<t> = PowerSeriesRing(ZZ, prec)
return P((1+t)*(1-t^10)/(1-18*t+170*t^10-153*t^11)).list()
(GAP) a:=[19, 342, 6156, 110808, 1994544, 35901792, 646232256, 11632180608, 209379250944, 3768826516821];; for n in [11..20] do a[n]:=17*Sum([1..9], j-> a[n-j]) -153*a[n-10]; od; Concatenation([1], a); # G. C. Greubel, Sep 24 2019
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|