A332651 Number of polygonal cacti on n unlabeled nodes with every polygon having an even number of edges.

1, 1, 0, 0, 1, 0, 1, 1, 1, 1, 4, 2, 7, 9, 14, 26, 48, 71, 154, 243, 478, 894, 1631, 3149, 6062, 11295, 22469, 42900, 83528, 164829, 321012, 632960, 1255613, 2472803, 4928140, 9808439, 19533534, 39134059, 78345317, 157177556, 316398963, 636790282, 1284910954

Offset: 0

Author

Andrew Howroyd, Feb 18 2020

Keywords

• nonn

Comments

Bridges are disallowed.

Examples

			a(6) = 1 corresponding with a hexagon.
a(7) = 1 corresponding with two quadrilaterals joined at a node.
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..200
• Wikipedia, Cactus graph
• Index entries for sequences related to cacti

Crossrefs

Cf. A000083, A035085, A091487, A332649, A332650.

Programs

PARI

\\ See A332650 for UCacti.
seq(n)={concat([1], UCacti(vector(n, i, i>2&&i%2==0)))}