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A306351
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Number of ways to split an n-cycle into connected subgraphs all having at least 4 vertices.
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8
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1, 0, 0, 0, 1, 1, 1, 1, 5, 10, 16, 23, 35, 53, 78, 111, 157, 222, 313, 438, 610, 848, 1178, 1634, 2263, 3131, 4330, 5986, 8272, 11427, 15782, 21794, 30093, 41548, 57359, 79183, 109307, 150887, 208279, 287496, 396838, 547761, 756077, 1043611, 1440488, 1988289
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OFFSET
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0,9
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LINKS
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FORMULA
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G.f.: (2*x^9-3*x^8+x^3-3*x^2+3*x-1)/((x^4+x-1)*(x-1)^2). - Alois P. Heinz, Feb 10 2019
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EXAMPLE
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The a(7) = 1 through a(9) = 10 partitions:
{{1234567}} {{12345678}} {{123456789}}
{{1234}{5678}} {{1234}{56789}}
{{1238}{4567}} {{12345}{6789}}
{{1278}{3456}} {{12349}{5678}}
{{1678}{2345}} {{12389}{4567}}
{{1239}{45678}}
{{12789}{3456}}
{{1289}{34567}}
{{16789}{2345}}
{{1789}{23456}}
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MATHEMATICA
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cycedsprop[n_, k_]:=Union[Sort/@Join@@Table[1+Mod[Range[i, j]-1, n], {i, n}, {j, i+k, n+i-1}]];
spsu[_, {}]:={{}}; spsu[foo_, set:{i_, ___}]:=Join@@Function[s, Prepend[#, s]&/@spsu[Select[foo, Complement[#, Complement[set, s]]=={}&], Complement[set, s]]]/@Cases[foo, {i, ___}];
Table[Length[spsu[cycedsprop[n, 3], Range[n]]], {n, 15}]
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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