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A323950 Number of ways to split an n-cycle into connected subgraphs, none having exactly two vertices. 9
1, 1, 1, 2, 6, 12, 23, 44, 82, 149, 267, 475, 841, 1484, 2613, 4595, 8074, 14180, 24896, 43702, 76705, 134622, 236260, 414623, 727629, 1276917, 2240851, 3932438, 6900967, 12110373, 21252244, 37295110, 65448378, 114853920, 201554603, 353703696, 620706742 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Table of n, a(n) for n=0..36.

Index entries for linear recurrences with constant coefficients, signature (4,-6,5,-3,1).

FORMULA

G.f.: (x^7-3*x^6+3*x^5-2*x^4+x^3-3*x^2+3*x-1)/((x^3-x^2+2*x-1)*(x-1)^2). - Alois P. Heinz, Feb 10 2019

EXAMPLE

The a(1) = 1 through a(5) = 12 partitions:

  {{1}}  {{1}{2}}  {{123}}      {{1234}}        {{12345}}

                   {{1}{2}{3}}  {{1}{234}}      {{1}{2345}}

                                {{123}{4}}      {{1234}{5}}

                                {{124}{3}}      {{1235}{4}}

                                {{134}{2}}      {{1245}{3}}

                                {{1}{2}{3}{4}}  {{1345}{2}}

                                                {{1}{2}{345}}

                                                {{1}{234}{5}}

                                                {{123}{4}{5}}

                                                {{125}{3}{4}}

                                                {{145}{2}{3}}

                                                {{1}{2}{3}{4}{5}}

MATHEMATICA

cyceds[n_, k_]:=Union[Sort/@Join@@Table[1+Mod[Range[i, j]-1, n], {i, n}, {j, Prepend[Range[i+k, n+i-1], i]}]];

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[cyceds[n, 2], Range[n]]], {n, 15}]

CROSSREFS

Cf. A000325, A001610, A001680, A005251, A066982, A306351, A323950, A323951, A323952, A323954.

Sequence in context: A192703 A192969 A294532 * A291014 A257479 A307740

Adjacent sequences:  A323947 A323948 A323949 * A323951 A323952 A323953

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 15 08:55 EST 2019. Contains 329144 sequences. (Running on oeis4.)