A253490 Number of (n+1) X (3+1) 0..2 arrays with every 2 X 2 subblock diagonal minus antidiagonal sum nondecreasing horizontally, vertically and ne-to-sw antidiagonally.

1388, 3090, 4196, 6931, 13528, 29370, 68992, 172050, 449608, 1219050, 3400912, 9693570, 28065688, 82170330, 242460832, 719285490, 2141665768, 6392619210, 19113104752, 57209811810, 171370433848, 513593301690, 1539743908672

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>7.

Empirical: a(n) = 49*3^(n-1) + 494*2^(n-1) + 1655 for n>4.

Conjectures from Colin Barker, Dec 15 2018: (Start)

G.f.: x*(1388 - 5238*x + 924*x^2 + 7417*x^3 - 442*x^4 - 733*x^5 - 6*x^6) / ((1 - x)*(1 - 2*x)*(1 - 3*x)).

a(n) = 1655 + 247*2^n + 49*3^(n-1) for n>4.

(End)

Example

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

Crossrefs

Column 3 of A253495.

Sequence in context: A200971 A259722 A253497 * A253451 A281164 A250816

Adjacent sequences: A253487 A253488 A253489 * A253491 A253492 A253493

Keyword

nonn

Author

R. H. Hardin, Jan 02 2015

Status

approved