|
|
A162785
|
|
Number of reduced words of length n in Coxeter group on 15 generators S_i with relations (S_i)^2 = (S_i S_j)^3 = I.
|
|
2
|
|
|
1, 15, 210, 2835, 38220, 514605, 6928740, 93285465, 1255955610, 16909618635, 227663487870, 3065158424055, 41267909559240, 555612506386665, 7480515990707760, 100714290692336685, 1355971748798391270
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
COMMENTS
|
The initial terms coincide with those of A170734, although the two sequences are eventually different.
Computed with MAGMA using commands similar to those used to compute A154638.
|
|
LINKS
|
|
|
FORMULA
|
G.f.: (t^3 + 2*t^2 + 2*t + 1)/(91*t^3 - 13*t^2 - 13*t + 1).
G.f.: (1+x)*(1-x^3)/(1 - 14*x + 104*x^3 - 91*x^4). - G. C. Greubel, Apr 26 2019
|
|
MATHEMATICA
|
CoefficientList[Series[(1+x)*(1-x^3)/(1-14*x+104*x^3-91*x^4), {x, 0, 20}], x] (* or *) coxG[{3, 91, -13}] (* The coxG program is at A169452 *) (* G. C. Greubel, Apr 26 2019 *)
|
|
PROG
|
(PARI) my(x='x+O('x^20)); Vec((1+x)*(1-x^3)/(1-14*x+104*x^3-91*x^4)) \\ G. C. Greubel, Apr 26 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^3)/(1-14*x+104*x^3-91*x^4) )); // G. C. Greubel, Apr 26 2019
(Sage) ((1+x)*(1-x^3)/(1-14*x+104*x^3-91*x^4)).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, Apr 26 2019
(GAP) a:=[15, 210, 2835];; for n in [4..20] do a[n]:=13*a[n-1]+13*a[n-2] -91*a[n-3]; od; Concatenation([1], a); # G. C. Greubel, Apr 26 2019
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|