A360879 -id:A360879 - cp's OEIS frontend

A046752 Triangle read by rows: T(n,k) is the number of unlabeled nonseparable (or 2-connected) loopless multigraphs with n edges on k nodes and degree >= 3 at each node, n >= 3, 2 <= k <= floor(2*n/3).

1, 1, 1, 1, 1, 2, 2, 1, 3, 5, 1, 4, 13, 4, 1, 6, 26, 24, 5, 1, 7, 47, 84, 38, 1, 9, 78, 233, 216, 23, 1, 11, 126, 557, 914, 314, 16, 1, 13, 188, 1193, 3077, 2270, 325, 1, 15, 276, 2355, 8915, 11592, 4015, 162, 1, 18, 391, 4370, 23008, 47079, 31443, 4495, 66

Offset: 3

N. J. A. Sloane

Original name: Triangle of number of homeomorphically irreducible stars with n edges and m nodes.

			Triangle begins:
  1;
  1;
  1,  1;
  1,  2,   2;
  1,  3,   5;
  1,  4,  13,    4;
  1,  6,  26,   24,    5;
  1,  7,  47,   84,   38;
  1,  9,  78,  233,  216,    23;
  1, 11, 126,  557,  914,   314,   16;
  1, 13, 188, 1193, 3077,  2270,  325;
  1, 15, 276, 2355, 8915, 11592, 4015, 162;
  ...

Andrew Howroyd, Table of n, a(n) for n = 3..93 (rows 3..18)
B. R. Heap, The enumeration of homeomorphically irreducible star graphs, J. Math. Phys., 7 (1966), 1582-1587.
Sean A. Irvine, Java program (github).

Row sums are A002935.
Diagonal sums are A360879.
Cf. A339160, A360866, A360870.

More terms from Sean A. Irvine, May 16 2020

Name edited and offset corrected by Andrew Howroyd, Feb 25 2023

A002935 Number of series-reduced star graphs with n edges.

Original entry on oeis.org

1, 1, 2, 5, 9, 22, 62, 177, 560, 1939, 7067, 27331, 110871, 468684, 2057161, 9341736

Offset: 3

N. J. A. Sloane

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

B. R. Heap, The enumeration of homeomorphically irreducible star graphs, J. Math. Phys., 7 (1966), 1582-1587.

Row sums of A046752.

Cf. A360879.

a(13)-a(17) from Sean A. Irvine, May 18 2020

a(18) from Andrew Howroyd, Feb 25 2023

A360868 Number of unlabeled connected loopless multigraphs with circuit rank n and degree >= 3 at each node.

Original entry on oeis.org

0, 1, 4, 23, 172, 1848, 25684

Offset: 1

Andrew Howroyd, Feb 25 2023

Diagonal sums of A360866.

Cf. A360864, A360867, A360879.

a(n) = Sum_{k>=1} A360866(n + k - 1, k).

cp's OEIS Frontend

A046752 Triangle read by rows: T(n,k) is the number of unlabeled nonseparable (or 2-connected) loopless multigraphs with n edges on k nodes and degree >= 3 at each node, n >= 3, 2 <= k <= floor(2*n/3).

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A002935 Number of series-reduced star graphs with n edges.

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Extensions

A360868 Number of unlabeled connected loopless multigraphs with circuit rank n and degree >= 3 at each node.

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Author

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