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 A057765 Number of factorable subsets of a 1 X n uniform grid. 3

%I #7 Jun 26 2022 07:35:17

%S 0,0,0,1,3,8,20,45,89,174,323,590,1048,1834,3135,5361,8977,14993,

%T 24859,41115,67329,110393,179756,292449,473375,766821,1237931,2001784,

%U 3225214,5198844,8380166,13515976,21751675,35055227,56462204,91065029,146752097,236629845,381499674

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

%C 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.

%H Sean A. Irvine, <a href="https://github.com/archmageirvine/joeis/blob/master/src/irvine/oeis/a057/A057765.java">Java program</a> (github)

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

%Y Cf. A057750.

%K nonn

%O 1,5

%A _John W. Layman_, Oct 30 2000

%E More terms from _Sean A. Irvine_, Jun 26 2022

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Last modified September 19 09:52 EDT 2024. Contains 376008 sequences. (Running on oeis4.)