A267960 Number of n X 1 0..2 arrays with every repeated value in every row and column greater than the previous repeated value.

3, 9, 24, 63, 159, 394, 957, 2292, 5419, 12678, 29385, 67560, 154215, 349770, 788741, 1769388, 3950499, 8782094, 19445313, 42898032, 94315743, 206709714, 451711869, 984397108, 2139750939, 4639901334, 10038505657, 21672089592, 46693408599

Offset

1,1

Comments

Column 1 of A267966.

Links

R. H. Hardin, Table of n, a(n) for n = 1..210

Formula

Empirical: a(n) = 6*a(n-1) - 9*a(n-2) - 8*a(n-3) + 24*a(n-4) - 16*a(n-6).

Conjectures from Colin Barker, Feb 25 2018: (Start)

G.f.: x*(3 - 9*x - 3*x^2 + 24*x^3 - 3*x^4 - 17*x^5) / ((1 + x)^2*(1 - 2*x)^4).

a(n) = (96*n + 2^n*(9*n*(n*(n+44)+445)+7622) + 640) / 7776 for n even.

a(n) = (2^n*(9*n*(n*(n+44)+445)+7622) - 32*(3*n+20)) / 7776 for n odd.

(End)

Example

Some solutions for n=8:
..1....0....1....1....0....2....0....0....2....1....1....1....2....0....2....0
..2....1....0....1....2....1....2....2....2....2....2....0....0....2....1....1
..0....0....2....2....0....1....0....1....1....0....2....1....1....1....0....1
..2....0....1....2....1....2....2....0....0....2....0....1....0....2....1....0
..0....1....1....0....2....1....0....0....2....0....2....0....2....0....1....2
..1....2....0....1....1....2....0....1....0....1....1....2....0....2....0....0
..2....0....2....0....0....1....2....2....2....0....0....2....1....0....2....1
..2....2....2....2....0....0....2....0....1....1....2....0....2....2....0....2

Crossrefs

Cf. A267966.

Sequence in context: A267465 A018788 A098690 * A268938 A090400 A123888

Adjacent sequences: A267957 A267958 A267959 * A267961 A267962 A267963

Keyword

nonn

Author

R. H. Hardin, Jan 22 2016

Status

approved