|
|
A166424
|
|
Number of reduced words of length n in Coxeter group on 30 generators S_i with relations (S_i)^2 = (S_i S_j)^11 = I.
|
|
1
|
|
|
1, 30, 870, 25230, 731670, 21218430, 615334470, 17844699630, 517496289270, 15007392388830, 435214379276070, 12621216999005595, 366015292971149640, 10614443496162974160, 307818861388715654040, 8926746980272446665760
(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
|
Index entries for linear recurrences with constant coefficients, signature (28,28,28,28,28,28,28,28,28,28,-406).
|
|
FORMULA
|
G.f.: (t^11 + 2*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)/(406*t^11 - 28*t^10 - 28*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).
a(n) = 28*Sum_{j=1..10} a(n-j) - 406*a(n-11).
G.f.: (1+x)*(1-x^11)/(1 - 29*x + 434*x^11 - 406*x^12). (End)
|
|
MATHEMATICA
|
With[{p=406, q=28}, CoefficientList[Series[(1+t)*(1-t^11)/(1-(q+1)*t + (p+q)*t^11-p*t^12), {t, 0, 40}], t]] (* G. C. Greubel, May 13 2016; Jul 25 2024 *)
|
|
PROG
|
(Magma)
R<x>:=PowerSeriesRing(Integers(), 30);
Coefficients(R!( (1+x)*(1-x^11)/(1-29*x+434*x^11-406*x^12) )); // G. C. Greubel, Jul 25 2024
(SageMath)
P.<x> = PowerSeriesRing(ZZ, prec)
return P( (1+x)*(1-x^11)/(1-29*x+434*x^11-406*x^12) ).list()
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|