A201500 Number of n X 3 0..1 arrays with every row and column running average nondecreasing rightwards and downwards, and the number of instances of each value within one of each other.

2, 2, 6, 5, 12, 8, 20, 13, 30, 18, 42, 25, 56, 32, 72, 41, 90, 50, 110, 61, 132, 72, 156, 85, 182, 98, 210, 113, 240, 128, 272, 145, 306, 162, 342, 181, 380, 200, 420, 221, 462, 242, 506, 265, 552, 288, 600, 313, 650, 338, 702, 365, 756, 392, 812, 421, 870, 450, 930, 481

Offset

1,1

Comments

Column 3 of A201503.

Links

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

Formula

Empirical: a(n) = 2*a(n-2) -2*a(n-6) +a(n-8).

Odd terms are A002378((n+1)/2).

Even terms are A000982((n+2)/2).

Empirical g.f.: x*(2 + 2*x + 2*x^2 + x^3 - 2*x^5 + x^7) / ((1 - x)^3*(1 + x)^3*(1 + x^2)). - Colin Barker, May 23 2018

Example

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

Crossrefs

Cf. A201503.

Sequence in context: A055924 A286278 A156563 * A054917 A111419 A360087

Adjacent sequences: A201497 A201498 A201499 * A201501 A201502 A201503

Keyword

nonn

Author

R. H. Hardin, Dec 02 2011

Status

approved