OFFSET
0,2
REFERENCES
N. Bourbaki, Groupes et alg. de Lie, Chap. 4, 5, 6. (The group is defined in Planche V.)
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
FORMULA
G.f.: (x^22 + 3*x^21 + 5*x^20 + 7*x^19 + 10*x^18 + 14*x^17 + 17*x^16 + 19*x^15 + 22*x^14 + 25*x^13 + 26*x^12 + 26*x^11 + 26*x^10 + 25*x^9 + 22*x^8 + 19*x^7 + 17*x^6 + 14*x^5 + 10*x^4 + 7*x^3 + 5*x^2 + 3*x + 1)/(x^22 - 4*x^21 + 6*x^20 - 4*x^19 + x^18 - x^15 + 4*x^14 - 6*x^13 + 4*x^12 - 2*x^11 + 4*x^10 - 6*x^9 + 4*x^8 - x^7 + x^4 - 4*x^3 + 6*x^2 - 4*x + 1)
EXAMPLE
Coxeter matrix:
. [1 2 3 2 2 2 2]
. [2 1 2 3 2 2 3]
. [3 2 1 3 2 2 2]
. [2 3 3 1 3 2 2]
. [2 2 2 3 1 3 2]
. [2 2 2 2 3 1 2]
. [2 3 2 2 2 2 1]
MATHEMATICA
CoefficientList[Series[(x^22 + 3 x^21 + 5 x^20 + 7 x^19 + 10 x^18 + 14 x^17 + 17 x^16 + 19 x^15 + 22 x^14 + 25 x^13 + 26 x^12 + 26 x^11 + 26 x^10 + 25 x^9 + 22 x^8 + 19 x^7 + 17 x^6 + 14 x^5 + 10 x^4 + 7 x^3 + 5 x^2 + 3 x + 1) / (x^22 - 4 x^21 + 6 x^20 - 4 x^19 + x^18 - x^15 + 4 x^14 - 6 x^13 + 4 x^12 - 2 x^11 + 4 x^10 - 6 x^9 + 4 x^8 - x^7 + x^4 - 4 x^3 + 6 x^2 - 4 x + 1), {x, 0, 50}], x] (* Vincenzo Librandi, Jun 09 2013 *)
PROG
(Magma)
Z := Integers();
C := SymmetricMatrix(
[1,
2, 1,
3, 2, 1,
2, 3, 3, 1,
2, 2, 2, 3, 1,
2, 2, 2, 2, 3, 1,
2, 3, 2, 2, 2, 2, 1]);
G := CoxeterGroup(GrpFPCox, C);
f := GrowthFunction(G);
T<z> := PowerSeriesRing(Z, 50);
Eltseq(T!f);
// Corrected by Klaus Brockhaus, Feb 12 2010
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
John Cannon and N. J. A. Sloane, Nov 29 2009
STATUS
approved