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

Author

Rodolfo Kurchan, Jan 09 2025

Keywords

• nonn
• more

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.

Examples

			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 |   |   |   |
+---+---+---+---+---+---+---+---+---+---+---+
		

Links

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

Crossrefs

Cf. A351516.

Extensions

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