

A057765


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


3



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
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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 3element 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



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



KEYWORD

nonn


AUTHOR



EXTENSIONS



STATUS

approved



