A253227 Number of (n+1) X (4+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.

335, 742, 914, 1498, 2543, 4490, 8216, 15476, 29780, 58148, 114620, 227276, 452276, 901940, 1800908, 3598460, 7193156, 14382116, 28759580, 57514028, 115022420, 230038676, 460070636, 920133980, 1840260068, 3680511620, 7361014076

Offset

1,1

Links

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

Formula

Empirical: a(n) = 5*a(n-1) - 9*a(n-2) + 7*a(n-3) - 2*a(n-4) for n>8.

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

G.f.: x*(335 - 933*x + 219*x^2 + 1261*x^3 - 1245*x^4 + 343*x^5 - 5*x^6 + x^7) / ((1 - x)^3*(1 - 2*x)).

a(n) = 188 + 1755*2^(n-5) + 60*n + 12*n^2 for n>4.

(End)

Example

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

Crossrefs

Column 4 of A253231.

Sequence in context: A119760 A046015 A184076 * A105099 A038648 A224533

Adjacent sequences: A253224 A253225 A253226 * A253228 A253229 A253230

Keyword

nonn

Author

R. H. Hardin, Dec 29 2014

Status

approved