A253449 Number of (n+1) X (1+1) 0..2 arrays with every 2 X 2 subblock diagonal minus antidiagonal sum nondecreasing horizontally and vertically.

81, 414, 1388, 3639, 8501, 19701, 48293, 126357, 346997, 982677, 2837237, 8295957, 24462197, 72541077, 215938037, 644449557, 1926625397, 5766435477, 17272430837, 51763547157, 155183156597, 465334505877, 1395573595637, 4185860948757

Offset

1,1

Comments

Column 1 of A253456.

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>10.

Empirical: a(n) = 400*3^(n-3) + 205*2^(n-1) + 2917 for n>7.

Empirical g.f.: x*(81 - 72*x - 205*x^2 - 621*x^3 - 549*x^4 + 396*x^5 + 1764*x^6 + 2304*x^7 + 1872*x^8 + 864*x^9) / ((1 - x)*(1 - 2*x)*(1 - 3*x)). - Colin Barker, Mar 20 2018

Example

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

Crossrefs

Cf. A253456.

Sequence in context: A253495 A253456 A236155 * A236148 A205986 A206668

Adjacent sequences: A253446 A253447 A253448 * A253450 A253451 A253452

Keyword

nonn

Author

R. H. Hardin, Jan 01 2015

Status

approved