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

1,4

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

Table of n, a(n) for n=1..13.

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.

Sequence in context: A296631 A255720 A014524 * A054488 A034349 A296797

Adjacent sequences: A098888 A098889 A098890 * A098892 A098893 A098894

Keyword

nonn,more

Author

Bernardo Recamán, Nov 08 2004

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

Status

approved