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A051291
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Whitney number of level n of the lattice of the ideals of the fence of order 2 n + 1.
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2
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1, 2, 3, 7, 17, 40, 97, 238, 587, 1458, 3640, 9124, 22951, 57904, 146461, 371281, 943045, 2399460, 6114555, 15603339, 39866932, 101976512, 261117378, 669239402, 1716737267, 4407306170, 11323050897, 29110603423, 74888578067
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| This is the second kind of Whitney numbers, which count elements, not to be confused with the first kind, which sum Mobius functions. - Thomas Zaslavsky (zaslav(AT)math.binghamton.edu), May 07 2008
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REFERENCES
| E. Munarini, N. Zagaglia Salvi, On the Rank Polynomial of the Lattice of Order Ideals of Fences and Crowns, Discrete Mathematics 259 (2002), 163-177.
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FORMULA
| G.f.: function = (1+2*t^2-t^3-(1-t)*sqrt(1-2*t-t^2-2*t^3+t^4))/(2*t*sqrt(1-2*t-t^2-2*t^3+t^4))
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EXAMPLE
| a(2) = 3 because the ideals of size 2 of the fence F(5) = { x1 < x2 > x3 < x4 > x5 } are x1x2, x1x3, x2x3.
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CROSSREFS
| Cf. A051286, A051292.
Sequence in context: A105554 A145230 A135364 * A178178 A143013 A113483
Adjacent sequences: A051288 A051289 A051290 * A051292 A051293 A051294
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KEYWORD
| nonn
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AUTHOR
| Emanuele Munarini (munarini(AT)mate.polimi.it)
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