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A057765 Number of factorable subsets of a 1 X n uniform grid. 2
0, 0, 0, 1, 3, 8, 20, 45, 89, 174, 323, 590, 1048, 1834, 3135, 5361, 8977, 14993, 24859 (list; graph; refs; listen; history; text; internal format)
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..19.

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

STATUS

approved

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Last modified November 30 20:17 EST 2021. Contains 349425 sequences. (Running on oeis4.)