A380025 Area of smallest rectangle of grid cells such that it is possible to mark a connected subset of the cells so that the lengths of runs of marked cells have lengths from 2 to n, each length appearing exactly once.

2, 6, 12, 15, 24, 35, 40, 54, 65, 77, 96, 112, 126, 150, 160

Offset

2,1

Comments

Runs may be horizontal or vertical and only lengths > 1 are considered.

In the puzzle, the best solutions are the ones with the most free space (fewest marked cells). In this sequence, only the area of the smallest rectangle is considered.

Terms a(6)-a(10) from George Sicherman.

a(11) from Giorgio Vecchi.

Links

Table of n, a(n) for n=2..16.

Rodolfo Kurchan, Crossword Polyominoes, Puzzle Fun, Problems (2025).

Example

a(11) = 77 from the following 7 x 11 rectangle:
2 to 11 = 77 (7 x 11) (30 free space).
+---+---+---+---+---+---+---+---+---+---+---+
| X | X | X | X | X | X | X | X | X | X | X |
+---+---+---+---+---+---+---+---+---+---+---+
|   |   |   |   |   | X | X | X | X |   |   |
+---+---+---+---+---+---+---+---+---+---+---+
| X | X | X | X | X | X | X | X | X | X |   |
+---+---+---+---+---+---+---+---+---+---+---+
|   |   |   |   |   | X | X |   | X |   |   |
+---+---+---+---+---+---+---+---+---+---+---+
| X | X | X | X | X | X | X | X | X |   |   |
+---+---+---+---+---+---+---+---+---+---+---+
|   |   |   |   |   | X |   |   | X |   |   |
+---+---+---+---+---+---+---+---+---+---+---+
| X | X | X | X | X | X | X | X |   |   |   |
+---+---+---+---+---+---+---+---+---+---+---+

Crossrefs

Cf. A351516.

Sequence in context: A242336 A285312 A065154 * A354757 A230482 A263546

Adjacent sequences: A380021 A380022 A380024 * A380026 A380027 A380028

Keyword

nonn,more

Author

Rodolfo Kurchan, Jan 09 2025

Extensions

a(12)-a(16) from Rodolfo Kurchan, Feb 01 2025

Status

approved