A227085 Number of n X 2 binary arrays indicating whether each 2 X 2 subblock of a larger binary array has lexicographically increasing rows and columns, for some larger (n+1) X 3 binary array with rows and columns of the latter in lexicographically nondecreasing order.

4, 12, 29, 62, 122, 225, 393, 655, 1048, 1618, 2421, 3524, 5006, 6959, 9489, 12717, 16780, 21832, 28045, 35610, 44738, 55661, 68633, 83931, 101856, 122734, 146917, 174784, 206742, 243227, 284705, 331673, 384660, 444228, 510973, 585526, 668554

Offset

1,1

Links

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

Formula

Empirical: a(n) = (1/120)*n^5 + (1/24)*n^4 + (5/24)*n^3 + (35/24)*n^2 + (77/60)*n + 1.

Conjectures from Colin Barker, Sep 07 2018: (Start)

G.f.: x*(2 - x)*(2 - 5*x + 6*x^2 - 3*x^3 + x^4) / (1 - x)^6.

a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n>6.

(End)

Example

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

Crossrefs

Column 2 of A227089.

Sequence in context: A086274 A174121 A128563 * A192978 A260546 A062421

Adjacent sequences: A227082 A227083 A227084 * A227086 A227087 A227088

Keyword

nonn

Author

R. H. Hardin, Jun 30 2013

Status

approved