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A089351 Number of planar partitions of n with trace 4. 1
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 (list; graph; refs; listen; history; text; internal format)
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 A257557 A124612

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

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Last modified July 21 02:02 EDT 2019. Contains 325189 sequences. (Running on oeis4.)