A091571 Poincaré series [or Poincare series] of the preprojective algebra of an extended Dynkin diagram of type E_8.

9, 16, 23, 30, 37, 44, 53, 60, 67, 74, 83, 90, 99, 106, 113, 118, 127, 134, 143, 150, 159, 164, 173, 180, 189, 194, 203, 208, 217, 224, 235, 240, 249, 254, 263, 268, 279, 284, 293, 298, 309, 314, 325, 330, 339, 342, 353, 358, 369, 374, 385, 388, 399, 404, 415

Offset: 0

Author

Paul Boddington, Jan 22 2004

Keywords

• easy
• nonn

Links

• I. Reiten, Dynkin diagrams and the representation theory of algebras, Notices of the AMS, Vol. 44, No 5 (1997) 546-556. [MR1444112]

Crossrefs

Cf. A087866, A091572, A091573, A091574, A091575, A091576, A091577.

Programs

Mathematica

CoefficientList[ Series[ (9-2x+9x^3-2x^4+9x^5-2x^7+9x^8) / (1-2x+x^2+x^3-2x^4+2x^5-2x^6+x^7+x^8-2x^9+x^10), {x, 0, 54}], x] (* Jean-François Alcover, Dec 02 2011 *)

Formula

a(n) = 7*(n+1) + 2*A087866(n).

G.f.: (7/(1-x)^2) + 2*(1-x^15)/((1-x^6)*(1-x^10)*(1-x)).