A183986 T(n,k) = 1/4 the number of (n+1) X (k+1) binary arrays with all 2 X 2 subblock sums the same.

4, 6, 6, 9, 8, 9, 15, 11, 11, 15, 25, 17, 14, 17, 25, 45, 27, 20, 20, 27, 45, 81, 47, 30, 26, 30, 47, 81, 153, 83, 50, 36, 36, 50, 83, 153, 289, 155, 86, 56, 46, 56, 86, 155, 289, 561, 291, 158, 92, 66, 66, 92, 158, 291, 561, 1089, 563, 294, 164, 102, 86, 102, 164, 294, 563

Offset: 1

Author

R. H. Hardin, Jan 08 2011

Keywords

• nonn
• tabl

Comments

Table starts

...4...6...9..15..25..45..81.153.289..561.1089.2145.4225.8385.16641.33153.66049

...6...8..11..17..27..47..83.155.291..563.1091.2147.4227.8387.16643.33155.66051

...9..11..14..20..30..50..86.158.294..566.1094.2150.4230.8390.16646.33158.66054

..15..17..20..26..36..56..92.164.300..572.1100.2156.4236.8396.16652.33164.66060

..25..27..30..36..46..66.102.174.310..582.1110.2166.4246.8406.16662.33174.66070

..45..47..50..56..66..86.122.194.330..602.1130.2186.4266.8426.16682.33194.66090

..81..83..86..92.102.122.158.230.366..638.1166.2222.4302.8462.16718.33230.66126

.153.155.158.164.174.194.230.302.438..710.1238.2294.4374.8534.16790.33302.66198

.289.291.294.300.310.330.366.438.574..846.1374.2430.4510.8670.16926.33438.66334

.561.563.566.572.582.602.638.710.846.1118.1646.2702.4782.8942.17198.33710.66606

Examples

			Some solutions for 6 X 5
..0..1..0..0..1....1..1..1..1..1....1..1..0..0..1....1..1..0..1..0
..1..0..1..1..0....1..0..1..0..1....0..0..1..1..0....0..0..1..0..1
..0..1..0..0..1....1..1..1..1..1....1..1..0..0..1....1..1..0..1..0
..1..0..1..1..0....0..1..0..1..0....0..0..1..1..0....0..0..1..0..1
..0..1..0..0..1....1..1..1..1..1....1..1..0..0..1....1..1..0..1..0
..1..0..1..1..0....0..1..0..1..0....0..0..1..1..0....0..0..1..0..1
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..683

Crossrefs

Columns 1..8 are A183978, A183979, A183980, A183981, A183982, A183983, A183984, A183985.

Main diagonal is A183977.

Cf. A184039, A184048.

Programs

PARI

T(n,k) = my(m=2, b=t->2^t-1); m^2 + (m-1)^2*(b(n-1) + b(k-1)) + (m-1)*(b((n-1)\2) + b(n\2) + b((k-1)\2) + b(k\2)) \\ Andrew Howroyd, Mar 09 2024

Formula

Empirical, for every row and column: a(n) = 3*a(n-1)-6*a(n-3)+4*a(n-4).

From Andrew Howroyd, Mar 09 2024: (Start)

The above empirical formula is correct.

T(n,k) = -2 + 2^(n-1) + 2^(k-1) + 2^(floor((n-1)/2)) + 2^(floor(n/2)) + 2^(floor((k-1)/2)) + 2^(floor(k/2)). (End)