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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 6
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 (list; table; graph; refs; listen; history; text; internal format)
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
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
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin Jul 03 2013
STATUS
approved

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Last modified May 29 22:36 EDT 2024. Contains 372954 sequences. (Running on oeis4.)