A057765 Number of factorable subsets of a 1 X n uniform grid.

0, 0, 0, 1, 3, 8, 20, 45, 89, 174, 323, 590, 1048, 1834, 3135, 5361, 8977, 14993, 24859, 41115, 67329, 110393, 179756, 292449, 473375, 766821, 1237931, 2001784, 3225214, 5198844, 8380166, 13515976, 21751675, 35055227, 56462204, 91065029, 146752097, 236629845, 381499674

Offset

1,5

Comments

A set is factorable if it is the union of at least two disjoint translated copies of a subset of at least two elements. E.g. the subset *..*.**..***.*.* of the 1x16 grid (where * denotes gridpoints in the selected subset and . denotes the remaining unselected gridpoints) is factorable into 3 copies of the 3-element subset *..*.*, as shown by displaying the factors by 1..1.12..232.3.3, where the numerals denote the elements of a particular translated copy.

Links

Table of n, a(n) for n=1..39.

Sean A. Irvine, Java program (github)

Example

The factorable subsets of (......) are (1122..), (11.22.), (.1122.), (1.12.2), (11..22), (.11.22), (..1122) and (111222), so a(6)=8.

Crossrefs

Cf. A057750.

Sequence in context: A109327 A192982 A096585 * A290866 A014628 A134393

Adjacent sequences: A057762 A057763 A057764 * A057766 A057767 A057768

Keyword

nonn

Author

John W. Layman, Oct 30 2000

Extensions

More terms from Sean A. Irvine, Jun 26 2022

Status

approved