A227252 Number of n X 2 binary arrays indicating whether each 2 X 2 subblock of a larger binary array has lexicographically nondecreasing rows and columns, for some larger (n+1) X 3 binary array with rows and columns of the latter in lexicographically nondecreasing order.

2, 3, 9, 23, 53, 113, 225, 421, 745, 1255, 2025, 3147, 4733, 6917, 9857, 13737, 18769, 25195, 33289, 43359, 55749, 70841, 89057, 110861, 136761, 167311, 203113, 244819, 293133, 348813, 412673, 485585, 568481, 662355, 768265, 887335, 1020757, 1169793

Offset

1,1

Links

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

Formula

Empirical: a(n) = (1/60)*n^5 - (1/12)*n^4 + (5/12)*n^3 + (1/12)*n^2 - (13/30)*n + 1 for n>1.

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

G.f.: x*(2 - 9*x + 21*x^2 - 26*x^3 + 20*x^4 - 7*x^5 + x^6) / (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>7.

(End)

Example

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

Crossrefs

Column 2 of A227256.

Sequence in context: A294910 A111240 A298407 * A274495 A299705 A318231

Adjacent sequences: A227249 A227250 A227251 * A227253 A227254 A227255

Keyword

nonn

Author

R. H. Hardin, Jul 04 2013

Status

approved