A258556 Number of (3+1) X (n+1) 0..1 arrays with every 2 X 2 subblock ne-sw antidiagonal difference nondecreasing horizontally and nw+se diagonal sum nondecreasing vertically.

104, 296, 598, 985, 1403, 1917, 2542, 3222, 3940, 4767, 5718, 6737, 7807, 8999, 10328, 11738, 13212, 14821, 16580, 18433, 20363, 22441, 24682, 27030, 29468, 32067, 34842, 37737, 40735, 43907, 47268, 50762, 54372, 58169, 62168, 66313, 70587, 75061, 79750

Offset

1,1

Links

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

Formula

Empirical: a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) + a(n-4) - 3*a(n-5) + 3*a(n-6) - a(n-7) for n>10.

Empirical g.f.: x*(104 - 16*x + 22*x^2 - 25*x^3 - 158*x^4 + 81*x^5 - 7*x^6 - 31*x^7 + 37*x^8 + 6*x^9) / ((1 - x)^4*(1 + x)*(1 + x^2)). - Colin Barker, Dec 22 2018

Example

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

Crossrefs

Row 3 of A258554.

Sequence in context: A271745 A046298 A298325 * A299218 A300032 A185763

Adjacent sequences: A258553 A258554 A258555 * A258557 A258558 A258559

Keyword

nonn

Author

R. H. Hardin, Jun 03 2015

Status

approved