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A001548
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Number of connected linear spaces with n (unlabeled) points.
(Formerly M1270 N0489)
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6
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1, 1, 0, 1, 1, 2, 4, 13, 42, 308, 4845, 227613, 28639650
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,6
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COMMENTS
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In any linear space any two distinct points belong to exactly one line. A linear space is disconnected if there exists a partition of the points of the space into two subsets such that for any two distinct points in a subset of the partition the unique line they both belong to is completely contained in that subset. - Michael Somos, Apr 24 2014
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REFERENCES
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L. M. Batten and A. Beutelspacher: The theory of finite linear spaces, Cambridge Univ. Press, 1993 (see the Appendix).
Doyen, Jean; Sur le nombre d'espaces linéaires non isomorphes de n points. Bull. Soc. Math. Belg. 19 1967 421-437.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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EXAMPLE
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a(2) = 0 because the unique linear space on two points can be partitioned into two single point subsets which disconnects the space vacuously. a(5) = 2 because there are two connected linear spaces with 5 points: one has only one line and the other has two lines with three points that intersect in one point that belongs to no other line while the other four points belong to three lines. - Michael Somos, Apr 24 2014
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MATHEMATICA
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A001200 = Cases[Import["https://oeis.org/A001200/b001200.txt", "Table"], {_, _}][[All, 2]];
(* EulerInvTransform is defined in A022562 *)
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CROSSREFS
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KEYWORD
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nonn,hard,nice,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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