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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 6
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 (list; table; graph; refs; listen; history; text; internal format)
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

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Last modified August 19 20:22 EDT 2022. Contains 356229 sequences. (Running on oeis4.)