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A006251
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Number of n-element posets which are unions of 2 chains.
(Formerly M1216)
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2
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1, 1, 2, 4, 10, 26, 75, 225, 711, 2311, 7725, 26313, 91141, 319749, 1134234, 4060128, 14648614, 53208998, 194423568, 714130372, 2635256408, 9764995800, 36320086418, 135548135854, 507434502474, 1904982684106, 7170113287574, 27051804890638, 102287657120454, 387558371409606, 1471212825012499, 5594771416613721
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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REFERENCES
| Problem 6342, Amer. Math. Monthly, 88 (1981), 294.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
R. P. Stanley, Enumerative Combinatorics, Cambridge, Vol. 2, 1999; see Problem 6.45.
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LINKS
| T. D. Noe, Table of n, a(n) for n=0..200
Index entries for sequences related to posets
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FORMULA
| G.f.: 4/(2-2*x+sqrt(1-4*x)+sqrt(1-4*x^2)).
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MATHEMATICA
| CoefficientList[Series[4/(2-2x+Sqrt[1-4x]+Sqrt[1-4x^2]), {x, 0, 40}], x] (* From Harvey P. Dale, May 12 2011 *)
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PROG
| (Pari) x='x+O('x^44) /* that many terms */
gf=4/(2-2*x+sqrt(1-4*x)+sqrt(1-4*x^2));
Vec(gf) /* show terms */ /* Joerg Arndt, Apr 20 2011 */
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CROSSREFS
| Sequence in context: A049143 A089404 A006123 * A049401 A148099 A007579
Adjacent sequences: A006248 A006249 A006250 * A006252 A006253 A006254
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KEYWORD
| nonn,nice,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| More terms from James A. Sellers (sellersj(AT)math.psu.edu), Aug 21 2000
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