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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.

User: Bertram Felgenhauer

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Bertram Felgenhauer has authored 2 sequences.

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

Original entry on oeis.org

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

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Author

Bertram Felgenhauer, Jun 11 2025

Keywords

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

Crossrefs

Column m=2 of A384764. Also column m=2 of A385862 (n X m yesnograms).
Cf. A242876.

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

Views

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.

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