A383345 Number of uniquely solveable n X 2 nonograms (hanjie).

1, 4, 14, 52, 210, 816, 3206, 12536, 48962, 191226, 746456, 2913544, 11371040, 44376798, 173181564, 675834086, 2637392942, 10292179494, 40164144690, 156736057740, 611644171812, 2386868430698, 9314465669046

Offset: 0

Author

Bertram Felgenhauer, Jun 11 2025

Keywords

• nonn
• hard

Comments

In this game there is an n X 2 grid where each square may or may not be filled. Each column and each row is labeled by the length of each successive block of filled squares, but without indication of the number of unfilled squares in between. The object is to determine which squares are filled.

The only ambiguous row hint is 1, which has the same solutions regardless of whether black or white squares are counted. So this is also the number of n X 2 "yesnograms".

Examples

			a(2) = 16-2 because out of the possible 2^(2*2) grids, only 10/01 and 01/10 have the same row and column clues.
		

Links

• Bertram Felgenhauer, Counting Nonograms.
• Wikipedia, Nonogram.

Crossrefs

Column m=2 of A384764. Also column m=2 of A385862 (n X m yesnograms).

Cf. A242876.