A227165 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 one or less, with rows and columns of the latter in lexicographically nondecreasing order.

2, 3, 3, 4, 8, 4, 5, 18, 18, 5, 6, 36, 62, 36, 6, 7, 66, 193, 193, 66, 7, 8, 113, 558, 944, 558, 113, 8, 9, 183, 1507, 4528, 4528, 1507, 183, 9, 10, 283, 3828, 20336, 37012, 20336, 3828, 283, 10, 11, 421, 9149, 85018, 283430, 283430, 85018, 9149, 421, 11, 12, 606

Offset: 1

Author

R. H. Hardin Jul 03 2013

Keywords

• nonn
• tabl

Comments

Table starts

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

..3...8....18......36.......66........113..........183..........283

..4..18....62.....193......558.......1507.........3828.........9149

..5..36...193.....944.....4528......20336........85018.......330949

..6..66...558....4528....37012.....283430......2010569.....13174529

..7.113..1507...20336...283430....3754497.....46389565....529521521

..8.183..3828...85018..2010569...46389565...1009485843..20376855291

..9.283..9149..330949.13174529..529521521..20376855291.732609096798

.10.421.20609.1200425.79606861.5548518625.377546087348

Examples

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

Links

• R. H. Hardin, Table of n, a(n) for n = 1..127

Formula

Empirical for column k:

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

k=2: a(n) = (1/24)*n^4 + (1/12)*n^3 + (23/24)*n^2 + (11/12)*n + 1

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

k=4: [polynomial of degree 19] for n>8

k=5: [polynomial of degree 39] for n>19