A188838 Number of n X 4 binary arrays without the pattern 0 1 diagonally or vertically.

16, 55, 121, 221, 364, 560, 820, 1156, 1581, 2109, 2755, 3535, 4466, 5566, 6854, 8350, 10075, 12051, 14301, 16849, 19720, 22940, 26536, 30536, 34969, 39865, 45255, 51171, 57646, 64714, 72410, 80770, 89831, 99631, 110209, 121605, 133860, 147016, 161116

Offset

1,1

Comments

Column 4 of A188843.

Links

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

Formula

Empirical: a(n) = (1/24)*n^4 + (11/12)*n^3 + (155/24)*n^2 + (163/12)*n - 6 for n>1.

Empirical g.f.: x*(16 - 25*x + 6*x^2 + 6*x^3 - x^4 - x^5) / (1 - x)^5. - Colin Barker, Apr 30 2018

Example

Some solutions for 3 X 4:
..1..1..1..1....0..1..0..1....1..1..1..0....1..1..0..0....1..1..0..0
..0..1..1..1....0..0..0..0....1..1..1..0....1..1..0..0....0..0..0..0
..0..0..1..1....0..0..0..0....1..1..1..0....1..1..0..0....0..0..0..0

Crossrefs

Cf. A188843.

Sequence in context: A224040 A244805 A362039 * A256049 A152096 A188701

Adjacent sequences: A188835 A188836 A188837 * A188839 A188840 A188841

Keyword

nonn

Author

R. H. Hardin, Apr 12 2011

Status

approved