A253489 Number of (n+1) X (2+1) 0..2 arrays with every 2 X 2 subblock diagonal minus antidiagonal sum nondecreasing horizontally, vertically and ne-to-sw antidiagonally.

414, 1377, 2640, 4720, 9654, 22236, 55362, 145428, 397002, 1114476, 3192402, 9277188, 27233562, 80506716, 239134242, 712632948, 2128361322, 6366010956, 19059888882, 57103380708, 171157572282, 513167579196, 1538892464322

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>8.

Empirical: a(n) = 49*3^(n-1) + 291*2^(n-1) + 1017 for n>5.

Empirical g.f.: x*(414 - 1107*x - 1068*x^2 + 1543*x^3 + 2112*x^4 + 392*x^5 - 180*x^6 - 72*x^7) / ((1 - x)*(1 - 2*x)*(1 - 3*x)). - Colin Barker, Dec 15 2018

Example

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

Crossrefs

Column 2 of A253495.

Sequence in context: A176381 A027661 A260472 * A253496 A253450 A236149

Adjacent sequences: A253486 A253487 A253488 * A253490 A253491 A253492

Keyword

nonn

Author

R. H. Hardin, Jan 02 2015

Status

approved