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

1,3

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.

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.

Example

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.

Crossrefs

Cf. A076184, A241706, A382180, A382194.

Sequence in context: A353577 A200778 A345355 * A132601 A394213 A047818

Adjacent sequences: A382280 A382281 A382282 * A382284 A382285 A382286

Keyword

nonn,tabf

Author

Pontus von Brömssen, Mar 22 2025

Status

approved