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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.
12
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
1,1
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
LINKS
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)
EXAMPLE
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
PROG
(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
CROSSREFS
Main diagonal is A183977.
Sequence in context: A201775 A199172 A323674 * A160995 A215454 A155750
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Jan 08 2011
STATUS
approved