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Search: id:A131518
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| A131518 |
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Number of partitions of the graph G_n (defined below) into "strokes". |
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+0
4
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| 2, 6, 14, 122, 362, 5282, 20582, 397154, 2027090, 46177922, 303147902, 7699478162, 63517159994, 1745540360930, 17676592058582, 517137940132802, 6290714838241442, 194139271606482434, 2782486941099788270, 90105513853333901042, 1495993248737211995402, 50671468195931300884322
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Here G_n = {V_n, E_n}, V_n = {v_1, v_2}, E_n = {e_1, e_2, ..., e_n}; for all i, e_i = v_1v_2.
Given an undirected graph G=(V,E), its partition into strokes is a collection of directed edge-disjoint paths (viewed as sets of directed edges) on V such that (i) union of any two paths is not a path; (ii) union of corresponding undirected paths is E.
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FORMULA
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For odd n, a(n)=2*A088009(n); for even n, a(n)=2*A088009(n)+n!*(n/2+1). The first term stands for partitions with paths starting and ending in different vertices. The second term (that exists only for even n) stands for partitions with paths starting and ending at the same vertex (there are at most 2 such paths starting and ending in v_1 and v_2 respectively, each path consists of even number of edges). - Max Alekseyev (maxale(AT)gmail.com), Sep 29 2007
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EXAMPLE
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G_2 : o=o, two edges exist between v_1 and v_2 .
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CROSSREFS
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Cf. A131519, A131520.
Sequence in context: A011455 A055691 A072171 this_sequence A130642 A119416 A134891
Adjacent sequences: A131515 A131516 A131517 this_sequence A131519 A131520 A131521
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KEYWORD
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nonn
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AUTHOR
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Yasutoshi Kohmoto zbi74583(AT)boat.zero.ad.jp, Aug 15 2007, Oct 03 2007
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EXTENSIONS
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More terms from Max Alekseyev (maxale(AT)gmail.com), Sep 29 2007
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