A253450 Number of (n+1) X (2+1) 0..2 arrays with every 2 X 2 subblock diagonal minus antidiagonal sum nondecreasing horizontally and vertically.

414, 1975, 4782, 8554, 15220, 31630, 74324, 188438, 502364, 1387310, 3928484, 11324678, 33058604, 97351070, 288409844, 857948918, 2559291644, 7648770830, 22888110404, 68547933158, 205411009484, 615767454590, 1846371222164

Offset

1,1

Links

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

Formula

Empirical: a(n) = 6*a(n-1) - 11*a(n-2) + 6*a(n-3) for n>9.

Empirical: a(n) = 529*3^(n-3) + 444*2^(n-1) + 3059 for n>6.

Empirical g.f.: x*(414 - 509*x - 2514*x^2 - 897*x^3 + 4648*x^4 + 5712*x^5 + 640*x^6 - 896*x^7 - 480*x^8) / ((1 - x)*(1 - 2*x)*(1 - 3*x)). - Colin Barker, Dec 13 2018

Example

Some solutions for n=4:
..0..1..1....1..1..1....0..1..2....0..1..1....0..2..2....1..2..2....0..2..2
..2..0..0....1..0..0....0..0..0....2..2..2....1..2..2....1..1..0....1..2..2
..2..0..0....2..1..1....2..1..1....2..2..2....2..2..2....1..1..0....0..0..0
..2..0..0....1..0..0....1..0..0....0..0..0....0..0..0....2..2..1....0..0..0
..2..0..0....0..0..1....1..0..0....1..1..1....1..1..2....0..0..1....2..2..2

Crossrefs

Column 2 of A253456.

Sequence in context: A260472 A253489 A253496 * A236149 A231312 A210304

Adjacent sequences: A253447 A253448 A253449 * A253451 A253452 A253453

Keyword

nonn

Author

R. H. Hardin, Jan 01 2015

Status

approved