Vladislav Bina has authored 2 sequences.
A208356
Number of labeled star-like graphs on n vertices.
Original entry on oeis.org
1, 2, 8, 61, 762, 13204, 300155, 8950176
Offset: 1
A179534
Number of labeled split graphs on n vertices.
Original entry on oeis.org
1, 2, 8, 58, 632, 9654, 202484, 5843954, 233064944, 12916716526, 998745087980, 108135391731690, 16434082400952296, 3513344943520006118, 1058030578581541945316, 449389062270642095128546, 269419653009366144571801568, 228157953744571034350576205790
Offset: 1
- V. Bina, Enumeration of Labeled Split Graphs and Counts of Important Superclasses. In Adacher L., Flamini, M., Leo, G., Nicosia, G., Pacifici, A., Picialli, V. (Eds.). CTW 2011, Villa Mondragone, Frascati, pp. 72-75 (2011).
- Andrew Howroyd, Table of n, a(n) for n = 1..100
- E. A. Bender, L. B. Richmond, and N. C. Wormald, Almost all chordal graphs split, J. Austral. Math. Soc. (Series A), 38 (1985), 214-221.
- V. Bina, Multidimensional probability distributions: Structure and learning, PHD Thesis. Fac. of Management, University of Economics in Prague (2011).
- Venkatesan Guruswami, Enumerative aspects of certain subclasses of perfect graphs, Discrete Mathematics 205 (1999), 97-117.
- J. M. Troyka, Split graphs: combinatorial species and asymptotics, arXiv:1803.07248 [math.CO], 2018-2019.
- J. M. Troyka, Split graphs: combinatorial species and asymptotics, Electron. J. Combin., 26 (2019), #P2.42.
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A179534 := proc(n) local a,k; a := 1 ; for k from 2 to n do a := a+binomial(n,k)*( (2^k-1)^(n-k) -add(j*k*binomial(n-k,j)*(2^(k-1)-1)^(n-k-j)/(j+1), j=1..n-k) ) end do: a ; end proc: # R. J. Mathar, Jun 21 2011
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a[n_] := 1 + Sum[Binomial[n,k]*((2^k-1)^(n-k) - Sum[j*k*Binomial[n-k,j]*(2^(k-1)-1)^(n-k-j)/(j+1), {j,1,n-k}]), {k,2, n}]; Array[a, 20] (* Stefano Spezia, Oct 29 2018 *)
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b(n) = {sum(k=0, n, binomial(n, k)*2^(k*(n-k)))} \\ A047863(n)
a(n) = b(n) - n*b(n-1) \\ Andrew Howroyd, Jun 06 2021
a(12)-a(16) corrected and terms a(17) and beyond from
Andrew Howroyd, Jun 06 2021
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