A253452 Number of (n+1) X (4+1) 0..2 arrays with every 2 X 2 subblock diagonal minus antidiagonal sum nondecreasing horizontally and vertically.

3639, 8554, 11147, 15730, 26831, 52912, 114717, 266911, 656997, 1694263, 4540077, 12545551, 35498037, 102227623, 298160637, 877448191, 2598287877, 7726760983, 23044088397, 68859886831, 206034914517, 617015262343, 1848866835357

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) + 1039*2^(n-1) + 5372 for n>6.

Empirical g.f.: x*(3639 - 13280*x - 148*x^2 + 21108*x^3 + 3744*x^4 - 1926*x^5 - 1994*x^6 - 345*x^7 - 54*x^8) / ((1 - x)*(1 - 2*x)*(1 - 3*x)). - Colin Barker, Dec 13 2018

Example

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

Crossrefs

Column 4 of A253456.

Sequence in context: A239992 A253498 A253491 * A253464 A015294 A186870

Adjacent sequences: A253449 A253450 A253451 * A253453 A253454 A253455

Keyword

nonn

Author

R. H. Hardin, Jan 01 2015

Status

approved