|
|
A165515
|
|
Number of reduced words of length n in Coxeter group on 30 generators S_i with relations (S_i)^2 = (S_i S_j)^9 = I.
|
|
1
|
|
|
1, 30, 870, 25230, 731670, 21218430, 615334470, 17844699630, 517496289270, 15007392388395, 435214379250840, 12621216997908960, 366015292928763240, 10614443494626832560, 307818861335266403640, 8926746978464285228160
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
COMMENTS
|
The initial terms coincide with those of A170749, although the two sequences are eventually different.
Computed with MAGMA using commands similar to those used to compute A154638.
|
|
LINKS
|
|
|
FORMULA
|
G.f.: (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)/( 406*t^9 -28*t^8 -28*t^7 -28*t^6 -28*t^5 -28*t^4 -28*t^3 -28*t^2 -28*t + 1).
|
|
MAPLE
|
seq(coeff(series((1+t)*(1-t^9)/(1-29*t+434*t^9-406*t^10), t, n+1), t, n), n = 0 .. 20); # G. C. Greubel, Sep 16 2019
|
|
MATHEMATICA
|
CoefficientList[Series[(1+t)*(1-t^9)/(1-29*t+434*t^9-406*t^10), {t, 0, 20}], t] (* G. C. Greubel, Oct 21 2018 *)
|
|
PROG
|
(PARI) my(t='t+O('t^20)); Vec((1+t)*(1-t^9)/(1-29*t+434*t^9-406*t^10)) \\ G. C. Greubel, Oct 21 2018
(Magma) R<t>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+t)*(1-t^9)/(1-29*t+434*t^9-406*t^10) )); // G. C. Greubel, Oct 21 2018
(Sage)
P.<t> = PowerSeriesRing(ZZ, prec)
return P((1+t)*(1-t^9)/(1-29*t+434*t^9-406*t^10)).list()
(GAP) a:=[30, 870, 25230, 731670, 21218430, 615334470, 17844699630, 517496289270, 15007392388395];; for n in [10..20] do a[n]:=28*Sum([1..8], j-> a[n-j]) -406*a[n-6]; od; Concatenation([1], a); # G. C. Greubel, Sep 16 2019
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|