A253225 Number of (n+1) X (2+1) 0..1 arrays with every 2 X 2 subblock diagonal minimum minus antidiagonal minimum nondecreasing horizontally and diagonal maximum minus antidiagonal maximum nondecreasing vertically.

47, 132, 306, 742, 1775, 4158, 9551, 21591, 48179, 106371, 232787, 505683, 1091603, 2343699, 5008403, 10658835, 22601747, 47771667, 100679699, 211632147, 443809811, 928710675, 1939603475, 4043571219, 8415870995, 17489199123

Offset

1,1

Links

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

Formula

Empirical: a(n) = 5*a(n-1) - 8*a(n-2) + 4*a(n-3) for n>7.

Conjectures from Colin Barker, Dec 10 2018: (Start)

G.f.: x*(47 - 103*x + 22*x^2 + 80*x^3 - 15*x^4 - 5*x^5 - 7*x^6) / ((1 - x)*(1 - 2*x)^2).

a(n) = 19 + 377*2^(n-6) + 627*2^(n-6)*n for n>4.

(End)

Example

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

Crossrefs

Column 2 of A253231.

Sequence in context: A044298 A044679 A350863 * A039530 A288408 A095311

Adjacent sequences: A253222 A253223 A253224 * A253226 A253227 A253228

Keyword

nonn

Author

R. H. Hardin, Dec 29 2014

Status

approved