A309116 a(n) = number of cographs on n points.
1, 3, 25, 1299, 1974452, 94345468975, 152799292695935115, 10526127565809458484649781, 38375912431199015810067477044326371, 9002076475560099357419498216602893054297145089, 162015966626938926212463690033352243299416773774432388589099
Offset: 2
Keywords
Links
- Robert Haas, Cographs, arXiv:1905.12627 [math.GM], 2019, p. 3, 57.
- Robert Haas, Intersection Cographs and Aesthetics, Journal of Humanistic Mathematics, 12 (2022), 4-23.
- Marko Riedel, Colorings of the complete graph Kn with any number of swappable colors.
Programs
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Mathematica
cycleIndSymm[n_] := cycleIndSymm[n] = CoefficientRules[CycleIndexPolynomial[ SymmetricGroup[n], x /@ Range[n]], x /@ Range[n]]; cycleIndEdge[n_] := cycleIndEdge[n] = CoefficientRules[Sum[Last[t] With[{tt = First[t]}, With[{ind = Flatten@Position[tt, Except[0], Heads -> False]}, Product[x[LCM@@p]^(GCD@@p Times@@tt[[p]]), {p, Subsets[ind, {2}]}] Product[With[{e = tt[[k]]}, x[k]^(k e (e-1)/2 + Quotient[k-1, 2] e) If[EvenQ[k], x[k/2]^e, 1]], {k, ind}]]], {t, cycleIndSymm[n]}], x /@ Range[n (n-1)/2]]; v[n_, m_] := With[{dv = Divisors /@ Range[m]}, Sum[Last[a] With[{ra = Flatten@Position[First@a, Except[0], Heads -> False]}, Sum[Last[b] Product[(dv[[va]].b[[1, dv[[va]]]])^a[[1, va]], {va, ra}], {b, cycleIndSymm[m]}]], {a, cycleIndEdge[n]}]]; a[2] = 1; a[3] = 3; a[n_] := 1 + v[n, -1 + n (n-1)/2]; Table[a[n], {n, 2, 7}] (* Andrey Zabolotskiy, Feb 06 2024, after Marko Riedel *)
Extensions
a(6)-a(9) from Andrey Zabolotskiy, Aug 27 2022
a(10) from Andrey Zabolotskiy, Feb 06 2024
a(11)-a(12) from Andrey Zabolotskiy, Feb 26 2025
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