A275421 Triangle read by rows: T(n,k) = number of graphs with n edges and k connected components.
1, 1, 1, 3, 1, 1, 5, 4, 1, 1, 12, 8, 4, 1, 1, 30, 23, 9, 4, 1, 1, 79, 57, 26, 9, 4, 1, 1, 227, 160, 68, 27, 9, 4, 1, 1, 710, 456, 197, 71, 27, 9, 4, 1, 1, 2322, 1402, 567, 208, 72, 27, 9, 4, 1, 1, 8071, 4468, 1748, 604, 211, 72, 27, 9, 4, 1, 1, 29503, 15071, 5555, 1874
Offset: 1
Examples
1
1 1
3 1 1
5 4 1 1
12 8 4 1 1
30 23 9 4 1 1
79 57 26 9 4 1 1
227 160 68 27 9 4 1 1
710 456 197 71 27 9 4 1 1
2322 1402 567 208 72 27 9 4 1 1
8071 4468 1748 604 211 72 27 9 4 1 1
29503 15071 5555 1874 615 212 72 27 9 4 1
Links
- Alois P. Heinz, Rows n = 1..60, flattened
- Peter Steinbach, Field Guide to Simple Graphs, Volume 4, Table 1.1a, Part 1 (For Volumes 1, 2, 3, 4 of this book see A000088, A008406, A000055, A000664, respectively.)
- Index entries for triangles generated by the Multiset Transformation
Programs
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Mathematica
rows = 12; A002905 = Import["https://oeis.org/A002905/b002905.txt", "Table"][[All, 2]]; gf = Product[(1 - y x^j)^-A002905[[j+1]], {j, 1, rows}]; Rest[CoefficientList[#, y]]& /@ Rest[CoefficientList[gf + O[x]^(rows+1), x]] // Flatten (* Jean-François Alcover, May 09 2019, after Alois P. Heinz *)
Formula
T(n,1) = A002905(n).
T(n,k) = Sum_{c_i*N_i=n,i=1..k} binomial(T(N_i,1)+c_i-1,c_i) for 1
G.f.: Product_{j>=1} (1-y*x^j)^(-A002905(j)). - Alois P. Heinz, Apr 13 2017
Comments