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A220579 T(n,k)=Equals one maps: number of nXk binary arrays indicating the locations of corresponding elements equal to exactly one of their horizontal and antidiagonal neighbors in a random 0..1 nXk array.

%I A220579 #6 Jul 23 2025 01:14:48
%S A220579 1,2,1,4,8,1,8,21,32,1,16,115,91,128,1,32,371,1441,375,512,1,64,1504,
%T A220579 8334,17505,1487,2048,1,128,5240,64497,165130,205323,5835,8192,1,256,
%U A220579 19904,436288,2652007,3162375,2352642,22775,32768,1,512,71787,3036588
%N A220579 T(n,k)=Equals one maps: number of nXk binary arrays indicating the locations of corresponding elements equal to exactly one of their horizontal and antidiagonal neighbors in a random 0..1 nXk array.
%C A220579 Table starts
%C A220579 .1.......2.......4..........8..........16...........32...........64.........128
%C A220579 .1.......8......21........115.........371.........1504.........5240.......19904
%C A220579 .1......32......91.......1441........8334........64497.......436288.....3036588
%C A220579 .1.....128.....375......17505......165130......2652007.....33180533...450926562
%C A220579 .1.....512....1487.....205323.....3162375....106841503...2449921734.65126683335
%C A220579 .1....2048....5835....2352642....59690533...4239598056.178051989526
%C A220579 .1....8192...22775...26616961..1120269376.166807007000
%C A220579 .1...32768...88683..299065708.20961430054
%C A220579 .1..131072..344975.3347252663
%C A220579 .1..524288.1341395
%C A220579 .1.2097152
%C A220579 .1
%H A220579 R. H. Hardin, <a href="/A220579/b220579.txt">Table of n, a(n) for n = 1..82</a>
%e A220579 Some solutions for n=3 k=4
%e A220579 ..1..1..0..0....0..1..1..1....0..0..0..1....0..0..1..1....1..0..0..1
%e A220579 ..0..1..1..1....1..0..0..1....0..0..0..1....1..0..1..0....0..0..0..1
%e A220579 ..1..1..0..1....1..0..0..1....1..0..1..1....0..1..0..0....1..1..1..1
%Y A220579 Column 2 is A004171(n-1)
%Y A220579 Row 1 is A000079(n-1)
%K A220579 nonn,tabl
%O A220579 1,2
%A A220579 _R. H. Hardin_ Dec 16 2012