cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

A384764 Number of uniquely solveable n X m nonograms (hanjie), read by antidiagonals.

Original entry on oeis.org

1, 1, 1, 1, 2, 1, 1, 4, 4, 1, 1, 8, 14, 8, 1, 1, 16, 52, 52, 16, 1, 1, 32, 210, 384, 210, 32, 1, 1, 64, 816, 3152, 3152, 816, 64, 1, 1, 128, 3206, 24230, 52362, 24230, 3206, 128, 1, 1, 256, 12536, 189898, 814632, 814632, 189898, 12536, 256, 1, 1, 512, 48962, 1473674, 12819322, 25309575, 12819322, 1473674, 48962, 512, 1
Offset: 0

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Author

Bertram Felgenhauer, Jun 09 2025

Keywords

Comments

In this game there is an n X m 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.

Examples

			A(2,2) = 16-2 because out of the possible 2^(2*2) grids, only 10/01 and 01/10 have the same row and column clues.
Top left corner of the array:
  1,  1,    1,      1,        1,         1,           1, ...
  1,  2,    4,      8,       16,        32,          64, ...
  1,  4,   14,     52,      210,       816,        3206, ...
  1,  8,   52,    384,     3152,     24230,      189898, ...
  1, 16,  210,   3152,    52362,    814632,    12819322, ...
  1, 32,  816,  24230,   814632,  25309575,   794378773, ...
  1, 64, 3206, 189898, 12819322, 794378773, 49745060669, ...

Links

Crossrefs

Cf. A242876 (main diagonal), A000012 (column m=0), A000079 (column m=1), A383345 (column m=2).
Cf. A385862 (variant: uniquely solveable n X m yesnograms).

Formula

Basic properties include A(n,m) = A(m,n), A(n,m) <= 2^(n*m), A(0,n) = A(n,0) = 1, and A(1,n) = A(n,1) = 2^n.

A385862 Number of n X m yesnograms that can be solved uniquely, read by antidiagonals.

Original entry on oeis.org

1, 1, 1, 1, 2, 1, 1, 4, 4, 1, 1, 8, 14, 8, 1, 1, 16, 52, 52, 16, 1, 1, 32, 210, 368, 210, 32, 1, 1, 64, 816, 2992, 2992, 816, 64, 1, 1, 128, 3206, 23058, 49578, 23058, 3206, 128, 1, 1, 256, 12536, 179576, 775204, 775204, 179576, 12536, 256, 1, 1, 512, 48962, 1388978, 12129616, 24177516, 12129616, 1388978, 48962, 512, 1
Offset: 0

Views

Author

Karl W. Heuer, Aug 06 2025

Keywords

Comments

In a nonogram puzzle, there is a hidden bitonal grid (or 0/1 matrix), and each row and each column is labeled by the length of each successive block of foreground pixels, but without indication of the number of background pixels separating them; the object is to determine the grid contents. In this variant, called a "yesnogram", the pixel value that represents foreground for row clues is the complement of the value that represents foreground for column clues.

Examples

			For the 3 X 4 grid shown below, the row clues (counting runs of 0s) and the column clues (counting runs of 1s) are sufficient to reconstruct the grid, so this is one of the 2992 solvable grids counted in A(3, 4).
       | 1 3 1 2
   ----+--------
   1   | 0 1 1 1
   1 1 | 0 1 0 1
   2   | 1 1 0 0
Top left corner of the array:
  1,  1,   1,     1,      1,        1,         1, ...
  1,  2,   4,     8,     16,       32,        64, ...
  1,  4,  14,    52,    210,      816,      3206, ...
  1,  8,  52,   368,   2992,    23058,    179576, ...
  1, 16, 210,  2992,  49578,   775204,  12129616, ...
  1, 32, 816, 23058, 775204, 24177516, 754845831, ...

Links

Crossrefs

Cf. A242876 (solvable n X n nonograms), A384764 (solvable n X m nonograms), A383345 (solvable n X 2 nonograms or yesnograms), A385861 (solvable n X n yesnograms).

Formula

A(0,n) = 1, and A(1,n) = 2^n. A(n,m) = A(m,n), because a grid is solvable iff its complement-transpose is solvable.

A385861 Number of n X n yesnograms that can be solved uniquely.

Original entry on oeis.org

1, 2, 14, 368, 49578, 24177516, 46985524156
Offset: 0

Views

Author

Karl W. Heuer, Aug 06 2025

Keywords

Comments

A nonogram provides row and column clues indicating runs of black pixels, treating white as blank. In this variant (called a "yesnogram"), the row clues instead indicate runs of white pixels, treating black as blank. Column clues remain unchanged from the standard nonogram.

Examples

			a(2) = 14 because, of the 16 2 X 2 grids, 10/01 and 01/10 would have the same set of clues; the other 14 are solvable.

Links

Crossrefs

Main diagonal of A385862.
Cf. A242876 (solvable n X n nonograms), A384764 (solvable n X m nonograms), A383345 (solvable n X 2 nonograms or yesnograms).
Showing 1-3 of 3 results.

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