|
|
A163514
|
|
Number of reduced words of length n in Coxeter group on 22 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I.
|
|
1
|
|
|
1, 22, 462, 9702, 203742, 4278351, 89840520, 1886549280, 39615400440, 831878586000, 17468509071090, 366818925627000, 7702782398341800, 161749714998425400, 3396561002126245800, 71323937982067871100
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
COMMENTS
|
The initial terms coincide with those of A170741, although the two sequences are eventually different.
Computed with MAGMA using commands similar to those used to compute A154638.
|
|
LINKS
|
|
|
FORMULA
|
G.f.: (t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(210*t^5 - 20*t^4 - 20*t^3 - 20*t^2 - 20*t + 1).
|
|
MATHEMATICA
|
CoefficientList[Series[(1+x)*(1-x^5)/(1-21*x+230*x^5-210*x^6), {x, 0, 20}], x] (* G. C. Greubel, Jul 27 2017 *)
|
|
PROG
|
(PARI) my(x='x+O('x^20)); Vec((1+x)*(1-x^5)/(1-21*x+230*x^5-210*x^6)) \\ G. C. Greubel, Jul 27 2017
(Magma) R<x>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^5)/(1-21*x+230*x^5-210*x^6) )); // G. C. Greubel, May 16 2019
(Sage) ((1+x)*(1-x^5)/(1-21*x+230*x^5-210*x^6)).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, May 16 2019
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|