A266930 Number of n X 3 binary arrays with rows lexicographically nondecreasing and columns lexicographically nondecreasing and row sums nondecreasing and column sums nonincreasing.

2, 4, 9, 20, 44, 92, 182, 340, 605, 1028, 1680, 2651, 4058, 6045, 8793, 12518, 17484, 24001, 32438, 43222, 56853, 73901, 95024, 120965, 152570, 190786, 236681, 291440, 356388, 432986, 522854, 627768, 749685, 890738, 1053264, 1239799, 1453106

Offset

1,1

Links

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

Formula

Empirical: a(n) = 4*a(n-1) - 4*a(n-2) - 3*a(n-3) + 6*a(n-4) - 6*a(n-7) + 3*a(n-8) + 4*a(n-9) - 4*a(n-10) + a(n-11).

Empirical g.f.: x*(2 - 4*x + x^2 + 6*x^3 - x^5 - 4*x^6 + 4*x^7 + 3*x^8 - 4*x^9 + x^10) / ((1 - x)^7*(1 + x)^2*(1 + x + x^2)). - Colin Barker, Jan 10 2019.

Example

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

Crossrefs

Column 3 of A266935.

Sequence in context: A175104 A123720 A179744 * A034007 A109975 A129891

Adjacent sequences: A266927 A266928 A266929 * A266931 A266932 A266933

Keyword

nonn

Author

R. H. Hardin, Jan 06 2016

Status

approved