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

3,6

Comments

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

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).

Example

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;
  ...

Crossrefs

Row sums are A002935.

Diagonal sums are A360879.

Cf. A339160, A360866, A360870.

Sequence in context: A266504 A111375 A165997 * A086350 A239830 A140767

Adjacent sequences: A046749 A046750 A046751 * A046753 A046754 A046755

Keyword

nonn,nice,tabf

Author

N. J. A. Sloane

Extensions

More terms from Sean A. Irvine, May 16 2020

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

Status

approved