A360880 Triangle read by rows: T(n,k) is the number of unlabeled nonseparable (or 2-connected) multigraphs with n edges and k nodes, loops allowed, n >= 1, 2 <= k <= n + 1.

1, 2, 0, 4, 1, 0, 6, 2, 1, 0, 9, 6, 3, 1, 0, 12, 14, 13, 4, 1, 0, 16, 28, 39, 22, 5, 1, 0, 20, 52, 112, 98, 39, 6, 1, 0, 25, 93, 281, 383, 236, 63, 8, 1, 0, 30, 152, 655, 1304, 1220, 515, 102, 9, 1, 0, 36, 242, 1408, 3980, 5418, 3512, 1077, 153, 11, 1, 0

Offset: 1

Author

Andrew Howroyd, Feb 25 2023

Keywords

• nonn
• tabl

Examples

			Triangle T(n,k) begins (n edges >= 1, k vertices >= 2):
   1;
   2,   0;
   4,   1,   0;
   6,   2,   1,    0;
   9,   6,   3,    1,    0;
  12,  14,  13,    4,    1,   0;
  16,  28,  39,   22,    5,   1,   0;
  20,  52, 112,   98,   39,   6,   1, 0;
  25,  93, 281,  383,  236,  63,   8, 1, 0;
  30, 152, 655, 1304, 1220, 515, 102, 9, 1, 0;
  ...
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..190 (rows 1..19)

Crossrefs

Columns k=2..3 are A002620(n+1), A050531(n-3).

Row sums are A360881.

Cf. A290428, A322115, A339070, A339160, A360870.