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 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 (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..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

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Last modified August 8 06:45 EDT 2024. Contains 375020 sequences. (Running on oeis4.)