A339040
Number of unlabeled connected simple graphs with n edges rooted at two noninterchangeable vertices.
Original entry on oeis.org
1, 3, 10, 35, 125, 460, 1747, 6830, 27502, 113987, 485971, 2129956, 9591009, 44341610, 210345962, 1023182861, 5100235807, 26035673051, 136023990102, 726877123975, 3970461069738, 22156281667277, 126234185382902, 733899631974167, 4351500789211840
Offset: 1
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\\ See A339063 for G.
seq(n)={my(A=O(x*x^n), g=G(2*n, x+A, [])); Vec(G(2*n, x+A, [1, 1])/g - (G(2*n, x+A, [1])/g)^2)}
A339041
Number of unlabeled connected simple graphs with n edges rooted at two indistinguishable vertices.
Original entry on oeis.org
1, 2, 7, 21, 73, 255, 946, 3618, 14376, 58957, 249555, 1087828, 4878939, 22488282, 106432530, 516783762, 2572324160, 13116137104, 68461594211, 365559412868, 1995532789212, 11129600885183, 63381069498524, 368338847181336, 2183239817036378
Offset: 1
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\\ See A339063 for G.
seq(n)={my(A=O(x*x^n), g=G(2*n, x+A, []), gr=G(2*n, x+A, [1])/g); Vec(G(2*n, x+A, [1, 1])/g - gr^2 + G(2*n, x+A, [2])/g - subst(gr, x, x^2))/2}
A339038
Number of unlabeled connected loopless multigraphs with n edges rooted at one unoriented edge.
Original entry on oeis.org
1, 2, 7, 23, 88, 339, 1396, 5915, 26080, 118539, 555678, 2678458, 13262193, 67353325, 350493424, 1866989802, 10171394388, 56631507822, 322011612423, 1868702977253, 11061267210030, 66745602611831, 410360493588788, 2569318971123439, 16374787277199728, 106180292431149021
Offset: 1
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seq[n_] := (G[2n, x + O[x]^n, {1, 1}] + G[2n, x + O[x]^n, {2}])/G[2n, x + O[x]^n, {}] // CoefficientList[#/2, x]&;
seq[15] (* Jean-François Alcover, Dec 02 2020, after Andrew Howroyd's code for G in A339065 *)
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\\ See A339065 for G.
seq(n)={my(A=O(x*x^n)); Vec((G(2*n, x+A, [1,1]) + G(2*n, x+A, [2]))/G(2*n, x+A, []))/2}
A339039
Number of unlabeled connected simple graphs with n edges rooted at one distinguished vertex.
Original entry on oeis.org
1, 1, 2, 5, 13, 37, 114, 367, 1248, 4446, 16526, 63914, 256642, 1067388, 4590201, 20376849, 93240065, 439190047, 2126970482, 10579017047, 53983000003, 282345671127, 1512273916781, 8287870474339, 46438619162441, 265840311066579
Offset: 0
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\\ See A339063 for G.
seq(n)={my(A=O(x*x^n)); Vec(G(2*n, x+A, [1])/G(2*n, x+A, []))}
A339044
Number of unlabeled connected simple graphs with n edges rooted at one oriented edge.
Original entry on oeis.org
1, 2, 6, 18, 57, 188, 651, 2336, 8719, 33741, 135185, 559908, 2394326, 10557283, 47943126, 223987316, 1075455181, 5301593544, 26807904317, 138924912857, 737220195148, 4002876571636, 22221898966507, 126042573704637, 729944250603862, 4313430995825272
Offset: 1
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\\ See A339063 for G.
seq(n)={my(A=O(x*x^n)); Vec(G(2*n, x+A, [1, 1])/G(2*n, x+A, [])/(1+x))}
A126133
Number of edge-rooted unlabeled graphs with n edges.
Original entry on oeis.org
1, 2, 7, 21, 66, 210, 699, 2387, 8492, 31329, 120034, 477028, 1965016, 8377888, 36923184, 167972182, 787688821, 3802526173, 18873118341, 96195592212, 502953711022, 2694740822749, 14781176429303, 82931707378322
Offset: 1
a(3)=7: the triangular graph with one edge rooted. The disconnected graph of the connected linear graph with 3 nodes aside the connected graph with 2 nodes, 2 choices for the root. The three disconnected graphs with 3 graphs on 2 nodes, one of the three with the root. The connected star graph with one edge rooted. The connected linear graph with four nodes, 2 choices for the root. - _R. J. Mathar_, May 03 2018
- F. Harary and E. M. Palmer, Graphical Enumeration, Academic Press, NY, 1973.
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\\ See A339063 for G.
seq(n)={my(A=O(x*x^n)); Vec((G(2*n, x+A, [1, 1]) + G(2*n, x+A, [2]))/(2*(1+x)))} \\ Andrew Howroyd, Nov 21 2020
Showing 1-6 of 6 results.