A091572 Poincaré series [or Poincare series] of the preprojective algebra of an extended Dynkin diagram of type E_7.
8, 14, 20, 26, 34, 40, 48, 54, 62, 66, 74, 80, 90, 94, 102, 106, 116, 120, 130, 134, 144, 146, 156, 160, 172, 174, 184, 186, 198, 200, 212, 214, 226, 226, 238, 240, 254, 254, 266, 266, 280, 280, 294, 294, 308, 306, 320, 320, 336, 334, 348, 346, 362, 360, 376
Offset: 0
References
- I, Reiten, Dynkin diagrams and the representation theory of algebras, Notices of the AMS, Vol. 44, No 5.
Programs
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Mathematica
CoefficientList[ Series[ (8 + 6x + 6x^2 + 14x^3 + 6x^4 + 6x^5 + 8x^6) / (1 - x + x^3 - 2x^4 + x^5 - x^7 + x^8),{x,0,54}],x] (* Jean-François Alcover, Dec 02 2011 *)
Formula
a(n) = 6*(n+1) + 2*A087504(n).
G.f.: (6/(1-x)^2)+2*(1-x^9)/((1-x^4)*(1-x^6)*(1-x)).