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A131520
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Number of partitions of the graph G_n (defined below) into "strokes".
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2
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2, 6, 12, 22, 40, 74, 140, 270, 528, 1042, 2068, 4118, 8216, 16410, 32796, 65566, 131104, 262178, 524324, 1048614, 2097192, 4194346, 8388652, 16777262, 33554480, 67108914, 134217780, 268435510, 536870968, 1073741882, 2147483708
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| G_n = {V_n, E_n}, V_n = {v_1, v_2, ..., v_n}, E_n = {v_1v_2, v2_v_3, ..., v_{n-1}v_n, v_nv_1}
See the definition of "stroke" in A089243.
A partition of a graph G into strokes S_i must satisfy the following conditions, where H is a digraph on G:
o Union_{i} S_i = H
o i != j => S_i and S_j do not have a common edge
o i != j => S_i U S_j is not a directed path
o For all i, S_i is a dipath
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FORMULA
| a(n) = 2*(n-1) + 2^n.
G.f.: 2*x*(-1+x+x^2)/(-1+x)^2/(-1+2*x). - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 14 2007
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EXAMPLE
| Figure for G_4 : o-o-o-o-o Two vertices on both sides are the same.
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MATHEMATICA
| s=1; lst={}; Do[s+=(n+=s++)-6; AppendTo[lst, Abs[s]], {n, 1, 5!, 2}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Nov 15 2008]
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CROSSREFS
| Cf. A131518, A131519.
Sequence in context: A005819 A168193 A182977 * A086953 A101953 A084570
Adjacent sequences: A131517 A131518 A131519 * A131521 A131522 A131523
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KEYWORD
| nonn
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AUTHOR
| Yasutoshi Kohmoto zbi74583(AT)boat.zero.ad.jp, Aug 15 2007
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EXTENSIONS
| More terms from Max Alekseyev (maxale(AT)gmail.com), Sep 29 2007
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