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

%I A384764 #26 Aug 19 2025 23:05:51
%S A384764 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,
%T A384764 1,64,816,3152,3152,816,64,1,1,128,3206,24230,52362,24230,3206,128,1,
%U A384764 1,256,12536,189898,814632,814632,189898,12536,256,1,1,512,48962,1473674,12819322,25309575,12819322,1473674,48962,512,1
%N A384764 Number of uniquely solveable n X m nonograms (hanjie), read by antidiagonals.
%C A384764 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.
%H A384764 Bertram Felgenhauer, <a href="/A384764/b384764.txt">Antidiagonals n+m = 0..13, flattened</a>
%H A384764 Bertram Felgenhauer, <a href="https://int-e.eu/nono/">Counting Nonograms</a>.
%H A384764 Wikipedia, <a href="https://en.wikipedia.org/wiki/Nonogram">Nonogram</a>.
%F A384764 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.
%e A384764 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.
%e A384764 Top left corner of the array:
%e A384764   1,  1,    1,      1,        1,         1,           1, ...
%e A384764   1,  2,    4,      8,       16,        32,          64, ...
%e A384764   1,  4,   14,     52,      210,       816,        3206, ...
%e A384764   1,  8,   52,    384,     3152,     24230,      189898, ...
%e A384764   1, 16,  210,   3152,    52362,    814632,    12819322, ...
%e A384764   1, 32,  816,  24230,   814632,  25309575,   794378773, ...
%e A384764   1, 64, 3206, 189898, 12819322, 794378773, 49745060669, ...
%Y A384764 Cf. A242876 (main diagonal), A000012 (column m=0), A000079 (column m=1), A383345 (column m=2).
%Y A384764 Cf. A385862 (variant: uniquely solveable n X m yesnograms).
%K A384764 nonn,tabl,hard
%O A384764 0,5
%A A384764 _Bertram Felgenhauer_, Jun 09 2025