A253497 Number of (3+1) X (n+1) 0..2 arrays with every 2 X 2 subblock diagonal minus antidiagonal sum nondecreasing horizontally, vertically and ne-to-sw antidiagonally.

1388, 2640, 4196, 6476, 11937, 25715, 60586, 151946, 399466, 1088906, 3050986, 8724746, 25321066, 74260106, 219377386, 651329546, 1940386666, 5793959306, 17327479786, 51873646346, 155403356266, 465774906506, 1396454398186

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) = 400*3^(n-3) + 415*2^(n-1) + 1626 for n>6.

Empirical g.f.: x*(1388 - 5688*x + 3624*x^2 + 2012*x^3 + 3397*x^4 + 153*x^5 - 1253*x^6 - 327*x^7 - 54*x^8) / ((1 - x)*(1 - 2*x)*(1 - 3*x)). - Colin Barker, Dec 16 2018

Example

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

Crossrefs

Row 3 of A253495.

Sequence in context: A182123 A200971 A259722 * A253490 A253451 A281164

Adjacent sequences: A253494 A253495 A253496 * A253498 A253499 A253500

Keyword

nonn

Author

R. H. Hardin, Jan 02 2015

Status

approved