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

1,1

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

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

Example

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

Crossrefs

Sequence in context: A156353 A239849 A202560 * A173933 A351407 A193821

Adjacent sequences: A227162 A227163 A227164 * A227166 A227167 A227168

Keyword

nonn,tabl

Author

R. H. Hardin Jul 03 2013

Status

approved