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

4,2

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).

Links

Table of n, a(n) for n=4..40.

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).

Crossrefs

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

Sequence in context: A110524 A083404 A232497 * A005380 A309536 A257557

Adjacent sequences: A089348 A089349 A089350 * A089352 A089353 A089354

Keyword

easy,nonn

Author

Wouter Meeussen and Vladeta Jovovic, Dec 26 2003

Extensions

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

Status

approved