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

0,1

References

I, Reiten, Dynkin diagrams and the representation theory of algebras, Notices of the AMS, Vol. 44, No 5.

Links

Table of n, a(n) for n=0..54.

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)).

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 *)

Crossrefs

Cf. A087504, A091571, A091573, A091574, A091575, A091576, A091577.

Sequence in context: A136798 A172182 A091575 * A369644 A369659 A096786

Adjacent sequences: A091569 A091570 A091571 * A091573 A091574 A091575

Keyword

easy,nonn

Author

Paul Boddington, Jan 22 2004

Status

approved