A204645 Number of (n+1) X 3 0..1 arrays with column and row pair sums b(i,j)=a(i,j)+a(i,j-1) and c(i,j)=a(i,j)+a(i-1,j) nondecreasing in column and row directions, respectively.

16, 32, 56, 90, 137, 200, 283, 390, 526, 696, 906, 1162, 1471, 1840, 2277, 2790, 3388, 4080, 4876, 5786, 6821, 7992, 9311, 10790, 12442, 14280, 16318, 18570, 21051, 23776, 26761, 30022, 33576, 37440, 41632, 46170, 51073, 56360, 62051, 68166, 74726, 81752

Offset: 1

Author

R. H. Hardin, Jan 17 2012

Keywords

• nonn

Comments

Column 2 of A204651.

Examples

			Some solutions for n=5:
..0..0..0....0..0..1....0..0..0....0..0..0....0..0..0....0..0..1....0..1..1
..0..0..0....0..0..1....0..0..1....0..0..1....0..0..0....0..1..1....0..1..1
..0..0..0....0..0..1....0..1..1....0..0..1....0..0..0....0..1..1....0..1..1
..0..0..0....0..1..1....0..1..1....0..0..1....0..1..1....0..1..1....0..1..1
..0..0..1....0..1..1....0..1..1....0..0..1....1..1..1....1..1..1....0..1..1
..1..1..1....1..1..1....1..1..1....0..0..1....1..1..1....1..1..1....1..1..1
		

Links

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

Crossrefs

Cf. A204651.

Formula

Empirical: a(n) = 4*a(n-1) - 5*a(n-2) + 5*a(n-4) - 4*a(n-5) + a(n-6).

Conjectures from Colin Barker, Jun 08 2018: (Start)

G.f.: x*(16 - 32*x + 8*x^2 + 26*x^3 - 23*x^4 + 6*x^5) / ((1 - x)^5*(1 + x)).

a(n) = (576 + 704*n + 232*n^2 + 16*n^3 + 2*n^4)/96 for n even.

a(n) = (582 + 704*n + 232*n^2 + 16*n^3 + 2*n^4)/96 for n odd.

(End)