A098891 Define the n-omino graph to be the graph whose vertices are each of the n-ominoes, two of which are joined by an edge if one can be obtained from the other by cutting out one of the latter's component squares (thus obtaining an (n-1)-omino for most cases) and gluing it elsewhere. The sequence counts the edges in these graphs.

0, 0, 1, 8, 47, 266, 1339, 6544, 29837, 133495, 585002, 2542563, 10959656

Offset: 1

Author

Bernardo Recamán, Nov 08 2004

Keywords

• nonn
• more

Comments

In some cases the act of removing a component square (temporarily) disconnects the polyomino before the component is reattached elsewhere. - Sean A. Irvine, Apr 13 2020

See A367435 for the case where the cells remaining after detaching the square to be moved must be a connected polyomino. - Pontus von Brömssen, Nov 18 2023

Links

• Freddy Barrera, Picture for a(5), 2020.
• Freddy Barrera, Picture for a(6), 2020.
• Sean A. Irvine, Java program (github)
• FUNG Cheok Yin, Tetrominoes
• FUNG Cheok Yin, Maxima code for n = 4 and n = 5, Apr 13 2020

Crossrefs

Half the row sums of A367126.

Cf. A367435.

Extensions

a(4) corrected by FUNG Cheok Yin, Feb 11 2020

a(5) corrected and a(6)-a(12) from Sean A. Irvine and Freddy Barrera, Apr 13 2020

a(13) from Pontus von Brömssen, Nov 05 2023