A227263 T(n,k)=Number of nXk 0,1 arrays indicating 2X2 subblocks of some larger (n+1)X(k+1) binary array having a sum of two or less, with rows and columns of the latter in lexicographically nondecreasing order

2, 3, 3, 4, 9, 4, 5, 23, 23, 5, 6, 50, 98, 50, 6, 7, 96, 353, 353, 96, 7, 8, 168, 1111, 2201, 1111, 168, 8, 9, 274, 3136, 11932, 11932, 3136, 274, 9, 10, 423, 8065, 57146, 112349, 57146, 8065, 423, 10, 11, 625, 19146, 244818, 937865, 937865, 244818, 19146, 625, 11

Offset

1,1

Comments

Table starts

..2...3.....4.......5.........6...........7...........8...........9

..3...9....23......50........96.........168.........274.........423

..4..23....98.....353......1111........3136........8065.......19146

..5..50...353....2201.....11932.......57146......244818......951917

..6..96..1111...11932....112349......937865.....6961606....46364258

..7.168..3136...57146....937865....13855163...182525275..2147322451

..8.274..8065..244818...6961606...182525275..4307345460.90839025368

..9.423.19146..951917..46364258..2147322451.90839025368

.10.625.42385.3403038.280471755.22777463128

Links

R. H. Hardin, Table of n, a(n) for n = 1..112

Formula

Empirical for column k:

k=1: a(n) = n + 1

k=2: a(n) = (1/24)*n^4 + (5/12)*n^3 + (11/24)*n^2 + (13/12)*n + 1

k=3: [polynomial of degree 9] for n>5

k=4: [polynomial of degree 19] for n>9

k=5: [polynomial of degree 39] for n>20

Example

Some solutions for n=4 k=4
..1..1..0..0....1..1..1..1....1..1..1..1....1..1..1..0....1..1..1..1
..1..0..0..0....1..0..0..1....1..0..0..1....1..0..0..1....1..1..0..1
..1..1..1..0....1..0..0..1....1..1..0..1....0..0..1..1....1..0..1..1
..1..1..1..0....1..1..0..0....1..1..0..0....0..0..1..1....0..0..1..1

Crossrefs

Sequence in context: A130743 A263775 A206455 * A111574 A330510 A173590

Adjacent sequences: A227260 A227261 A227262 * A227264 A227265 A227266

Keyword

nonn,tabl

Author

R. H. Hardin Jul 04 2013

Status

approved