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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 November 17 13:33 EST 2019. Contains 329230 sequences. (Running on oeis4.)