A188839 Number of n X 5 binary arrays without the pattern 0 1 diagonally or vertically.

32, 144, 364, 728, 1288, 2108, 3264, 4845, 6954, 9709, 13244, 17710, 23276, 30130, 38480, 48555, 60606, 74907, 91756, 111476, 134416, 160952, 191488, 226457, 266322, 311577, 362748, 420394, 485108, 557518, 638288, 728119, 827750, 937959, 1059564

Offset

1,1

Comments

Column 5 of A188843.

Links

R. H. Hardin, Table of n, a(n) for n = 1..200

Formula

Empirical: a(n) = (1/120)*n^5 + (7/24)*n^4 + (89/24)*n^3 + (473/24)*n^2 + (1877/60)*n - 33 for n>2.

Empirical g.f.: x*(32 - 48*x - 20*x^2 + 64*x^3 - 20*x^4 - 12*x^5 + 4*x^6 + x^7) / (1 - x)^6. - Colin Barker, Apr 30 2018

Example

Some solutions for 3 X 5:
..1..1..0..0..1....0..1..1..1..1....1..1..1..0..1....1..1..1..1..1
..1..1..0..0..0....0..0..0..0..0....1..1..1..0..0....0..1..0..1..0
..0..1..0..0..0....0..0..0..0..0....1..0..1..0..0....0..0..0..0..0

Crossrefs

Cf. A188843.

Sequence in context: A048191 A363531 A224041 * A188702 A297342 A228758

Adjacent sequences: A188836 A188837 A188838 * A188840 A188841 A188842

Keyword

nonn

Author

R. H. Hardin, Apr 12 2011

Status

approved