A239231 Heyawake numbers: maximum number of painted cells in an n X n grid, such that no two painted cells are orthogonally adjacent and the unpainted cells form a contiguous area.

0, 1, 1, 4, 5, 9, 12, 17, 21, 27, 33, 41, 48, 56, 65, 75, 85, 96, 108, 121, 133, 146, 161, 176, 190, 208

Offset: 0

Author

Elliott Line, Mar 13 2014

Keywords

• nonn
• more

Comments

Inspired by the Japanese puzzle of the same name.

Examples

			If n=6, the painted cells could be A1, A3, A6, B5, C1, C3, D4, D6, E2, F1, F4, F6 (12 cells in all).
		

Links

• Wikipedia, Heyawake.

Crossrefs

Cf. A239072 (makes up the inner n-4 X n-4 square of the grid).

Formula

a(n) = A239072(n-4) + 2*n - 2 for n > 4.

Extensions

Some values corrected, incorrect values removed by Elliott Line, Aug 21 2014

a(16) and a(20) corrected by Elliott Line at the suggestion of Greg Malen, Sep 02 2020