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A057750 Number of non-factorable subsets of size >= 2 of a 1 X n uniform grid. 2
0, 1, 4, 10, 23, 49, 100, 202, 413, 839, 1713, 3493, 7130, 14535, 29617, 60158, 122077, 247132, 499409, 1007440, 2029801, 4083888, 8208828, 16484742, 33081031, 66342016, 132979769, 266433643, 533645668, 1068542949, 2139103450, 4281451287, 8568182883 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,3
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
FORMULA
a(n) = 2^n - (n+1) - A057765(n). - Sean A. Irvine, Jun 26 2022
EXAMPLE
The factorable subsets of (......) are (1122..), (11.22.), (.1122.), (1.12.2), (11..22), (.11.22), (..1122) and (111222) and there are seven subsets with fewer than 2 elements, so a(6)=2^6-8-7=49.
CROSSREFS
Cf. A057765.
Sequence in context: A158671 A001980 A266376 * A295059 A118645 A200759
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 April 22 18:11 EDT 2024. Contains 371906 sequences. (Running on oeis4.)