A123991 Expansion of o.g.f. (1-x^2+x^4)/((1-x)^2*(1-x^2)^4*(1-x^3)^4).

1, 2, 6, 14, 29, 56, 107, 186, 320, 530, 851, 1332, 2051, 3074, 4544, 6602, 9444, 13322, 18579, 25564, 34827, 46954, 62692, 82954, 108889, 141732, 183169, 235042, 299584, 379434, 477763, 598036, 744628, 922348, 1136838, 1394608, 1703246, 2071068, 2508084

Offset

0,2

Comments

Poincaré series [or Poincare series] P(C_{3,2}; x).

References

B. Broer, Hilbert series for modules of covariants, in Algebraic Groups and Their Generalizations..., Proc. Sympos. Pure Math., 56 (1994), Part I, 321-331.

Links

Peter J. C. Moses, Table of n, a(n) for n = 0..9999

Dragomir Z. Djokovic, Poincaré series [or Poincare series] of some pure and mixed trace algebras of two generic matrices. arXiv:math/0609262 [math.AC], 2006. See Table 3, lines 4 and 5, also Table 5, lines 1 and 2.

Y. Teranishi, The ring of invariants of matrices, Nagoya Math. J., 104 (1986), 149-161.

Index entries for linear recurrences with constant coefficients, signature (2, 3, -4, -10, 0, 24, 12, -27, -34, 11, 48, 11, -34, -27, 12, 24, 0, -10, -4, 3, 2, -1).

Formula

G.f.: (1+x^6)/((1-x)^2*(1-x^2)^3*(1-x^3)^4*(1-x^4)).

Mathematica

CoefficientList[Series[(1-x^2+x^4)/((1-x)^2(1-x^2)^4(1-x^3)^4), {x, 0, 40}], x] (* Harvey P. Dale, Dec 20 2014 *)

Crossrefs

Cf. A124636.

Sequence in context: A214907 A169948 A192705 * A112511 A143702 A063452

Adjacent sequences: A123988 A123989 A123990 * A123992 A123993 A123994

Keyword

nonn,easy

Author

N. J. A. Sloane, Dec 21 2006

Status

approved