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A089351
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Number of planar partitions of n with trace 4.
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1
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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; internal format)
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OFFSET
| 4,2
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COMMENTS
| Also number of partitions of n objects of 2 colors into 4 parts, each part containing at least one black object.
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REFERENCES
| G. E. Andrews, The Theory of Partitions, Addison-Wesley, 1976 (Ch. XI, exercise 5 and Ch. XII, exercise 5).
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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).
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CROSSREFS
| Column 4 of A089353. Cf. A000219, A005380, A005993 (trace 2), A050531 (trace 3).
Sequence in context: A077999 A110524 A083404 * A005380 A124612 A184697
Adjacent sequences: A089348 A089349 A089350 * A089352 A089353 A089354
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KEYWORD
| easy,nonn
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AUTHOR
| Wouter Meeussen and Vladeta Jovovic (vladeta(AT)eunet.rs), Dec 26 2003
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EXTENSIONS
| Edited and extended by Christian G. Bower (bowerc(AT)usa.net), Jan 08 2004
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