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

Author

N. J. A. Sloane

Keywords

• nonn
• nice
• tabf

Comments

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

Examples

			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;
  ...
		

Links

• 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).

Crossrefs

Row sums are A002935.

Diagonal sums are A360879.

Cf. A339160, A360866, A360870.

Extensions

More terms from Sean A. Irvine, May 16 2020

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