A089351 Number of planar partitions of n with trace 4.

1, 2, 6, 14, 33, 64, 127, 228, 404, 672, 1100, 1724, 2661, 3974, 5849, 8402, 11911, 16556, 22751, 30772, 41198, 54436, 71283, 92316, 118609, 150950, 190753, 239090, 297783, 368236, 452782, 553240, 672532, 812980, 978211, 1171144, 1396235

Offset: 4

Author

Wouter Meeussen and Vladeta Jovovic, Dec 26 2003

Keywords

• easy
• nonn

Comments

Also number of partitions of n objects of 2 colors into 4 parts, each part containing at least one black object.

References

• G. E. Andrews, The Theory of Partitions, Addison-Wesley, 1976 (Ch. XI, exercise 5 and Ch. XII, exercise 5).

Crossrefs

Column 4 of A089353. Cf. A000219, A005380, A005993 (trace 2), A050531 (trace 3).

Formula

G.f.: q^4*(q^12+q^10+2*q^9+4*q^8+2*q^7+4*q^6+2*q^5+4*q^4+2*q^3+q^2+1) / ((-1+q^4)^2*(-1+q^3)^2*(-1+q^2)^2*(-1+q)^2).

Extensions

Edited and extended by Christian G. Bower, Jan 08 2004