0,4

Inspired by the Japanese puzzle of the same name.

Wikipedia, Heyawake.

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

For n=6, the painted cells could be A1, A3, A6, B5, C1, C3, D4, D6, E2, F1, F4, F6 (a(6)=12 cells in all, equal to the lower bound given in the Formula section):

#.#..#

....#.

#.#...

...#.#

.#....

#..#.#

For n=7, a(7) is equal to the lower bound 17. The unique solution comes from the A239072(3) = 5 painted cells enclosed into a frame of unpainted cells and then into the outer frame in which every other cell is painted, including the corners:

#.#.#.#

.......

#.#.#.#

...#...

#.#.#.#

.......

#.#.#.#

Cf. A239072, A322125, A354673.

Sequence in context: A200535 A010405 A125603 * A078507 A060199 A229240

Adjacent sequences: A239228 A239229 A239230 * A239232 A239233 A239234

nonn,more

Elliott Line, Mar 13 2014

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

Entry edited by Andrei Zabolotskii, Feb 28 2026. The terms need independent verification.

approved