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Search: id:A131519
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| A131519 |
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Number of partitions of the graph G_n (defined below) into "strokes". |
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3
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| 1, 6, 66, 714, 7710, 83226, 898350, 9696810, 104667486, 1129781946, 12194877966, 131631637962, 1420833250878, 15336488688474, 165542216262126, 1786864380862314, 19287432460962078, 208188743880291834, 2247191437542514638, 24256207433904571146, 261821751919823278590
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Here G_n = {V_n, E_n}, V_n = {v_1, v_2,..., v_n}, E_n = {e_1, e_2, ..., e_{n-1}, f_1, f_2, ..., f_{n-1}}. For all i, e_i = f_i = v_iv_{i+1}
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 n>4, a(n) = 11*a(n-1) - 24*a(n-3). - Max Alekseyev (maxal(AT)cs.ucsd.edu), Sep 29 2007
G.f.: x*(2*x-1)*(6*x^2+3*x-1)/(1-11*x+24*x^3). - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 14 2007
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EXAMPLE
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Figure for G_5 : o=o=o=o=o
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CROSSREFS
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Cf. A131518, A131520.
Sequence in context: A119210 A119234 A119232 this_sequence A022024 A129554 A127857
Adjacent sequences: A131516 A131517 A131518 this_sequence A131520 A131521 A131522
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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 (maxal(AT)cs.ucsd.edu), Sep 29 2007
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