A382283 Number of square roots of connected square graphs in the order listed in A382194.

1, 1, 2, 1, 5, 1, 2, 3, 15, 1, 1, 2, 3, 4, 1, 3, 3, 15, 1, 1, 17, 60, 1, 2, 1, 2, 1, 1, 1, 1, 4, 2, 3, 2, 4, 11, 10, 11, 2, 1, 5, 3, 3, 6, 9, 8, 6, 1, 1, 19, 51, 3, 21, 1, 1, 3, 21, 2, 3, 113, 1, 11, 127, 374, 1, 1, 2, 3, 4, 1, 1, 2, 3, 4, 1, 1, 2, 1, 1, 1, 2

Offset: 1

Author

Pontus von Brömssen, Mar 22 2025

Keywords

• nonn
• tabf

Comments

A382194 lists all connected graphs that are squares, encoded as in A076184. a(n) is the number of unlabeled graphs whose squares are isomorphic to the n-th graph in A382194.

Examples

			As an irregular triangle, where row n >= 1 contains A382180(n) terms:
  1;
  1;
  2;
  1, 5;
  1, 2, 3, 15;
  1, 1, 2,  3, 4, 1, 3, 3, 15, 1, 1, 17, 60;
  ...
The last term on row n equals A241706(n)+1, the number of graphs whose square is the complete graph on n vertices.
		

Links

• Pontus von Brömssen, Table of n, a(n) for n = 1..1580 (for graphs on up to 9 vertices)
• Eric Weisstein's World of Mathematics, Graph Square.
• Wikipedia, Graph power.

Crossrefs

Cf. A076184, A241706, A382180, A382194.