A057750 Number of non-factorable subsets of size >= 2 of a 1 X n uniform grid.

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

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

Table of n, a(n) for n=1..33.

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 * A377823 A295059 A118645

Adjacent sequences: A057747 A057748 A057749 * A057751 A057752 A057753

Keyword

nonn

Author

John W. Layman, Oct 30 2000

Extensions

More terms from Sean A. Irvine, Jun 26 2022

Status

approved