A253393 Number of (n+1) X (4+1) 0..1 arrays with every 2 X 2 subblock antidiagonal maximum minus diagonal minimum nondecreasing horizontally and diagonal maximum minus antidiagonal minimum nondecreasing vertically.

180, 197, 246, 346, 465, 632, 823, 1071, 1351, 1695, 2079, 2535, 3039, 3623, 4263, 4991, 5783, 6671, 7631, 8695, 9839, 11095, 12439, 13903, 15463, 17151, 18943, 20871, 22911, 25095, 27399, 29855, 32439, 35183, 38063, 41111, 44303, 47671, 51191, 54895

Offset

1,1

Links

R. H. Hardin, Table of n, a(n) for n = 1..210

Formula

Empirical: a(n) = 3*a(n-1) - 2*a(n-2) - 2*a(n-3) + 3*a(n-4) - a(n-5) for n>11.

Empirical for n mod 2 = 0: a(n) = (2/3)*n^3 + 7*n^2 + (70/3)*n + 95 for n>6.

Empirical for n mod 2 = 1: a(n) = (2/3)*n^3 + 7*n^2 + (70/3)*n + 88 for n>6.

Empirical g.f.: x*(180 - 343*x + 15*x^2 + 362*x^3 - 227*x^4 + 10*x^5 + 8*x^6 + 4*x^7 - x^8 - x^9 + x^10) / ((1 - x)^4*(1 + x)). - Colin Barker, Dec 11 2018

Example

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

Crossrefs

Column 4 of A253397.

Sequence in context: A053325 A119542 A154360 * A260265 A117551 A068545

Adjacent sequences: A253390 A253391 A253392 * A253394 A253395 A253396

Keyword

nonn

Author

R. H. Hardin, Dec 31 2014

Status

approved