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 A323951 Number of ways to split an n-cycle into connected subgraphs, all having at least three vertices. 7
 1, 0, 0, 1, 1, 1, 4, 8, 13, 22, 36, 56, 86, 131, 197, 294, 437, 647, 955, 1407, 2070, 3042, 4467, 6556, 9618, 14106, 20684, 30325, 44455, 65164, 95515, 139997, 205189, 300733, 440760, 645980, 946745, 1387538, 2033552, 2980332, 4367906, 6401495, 9381865, 13749810 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,7 LINKS Table of n, a(n) for n=0..43. Index entries for linear recurrences with constant coefficients, signature (3,-3,2,-2,1). FORMULA G.f.: (x^7-2*x^6+x^3-3*x^2+3*x-1)/((x^3+x-1)*(x-1)^2). - Alois P. Heinz, Feb 10 2019 EXAMPLE The a(3) = 1 through a(7) = 8 partitions: {{123}} {{1234}} {{12345}} {{123456}} {{1234567}} {{123}{456}} {{123}{4567}} {{126}{345}} {{1234}{567}} {{156}{234}} {{1237}{456}} {{1267}{345}} {{127}{3456}} {{1567}{234}} {{167}{2345}} MATHEMATICA 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, 2], Range[n]]], {n, 15}] CROSSREFS Cf. A000325, A001610, A001680, A005251, A066982, A306351, A323950, A323952, A323954. Sequence in context: A007882 A265258 A009852 * A080003 A033016 A027008 Adjacent sequences: A323948 A323949 A323950 * A323952 A323953 A323954 KEYWORD nonn,easy AUTHOR Gus Wiseman, Feb 10 2019 EXTENSIONS More terms from Alois P. Heinz, Feb 10 2019 STATUS approved

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Last modified April 21 01:42 EDT 2024. Contains 371850 sequences. (Running on oeis4.)