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

1,1

Comments

Column 2 of A204651.

Links

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

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)

Example

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

Crossrefs

Cf. A204651.

Sequence in context: A260050 A224544 A255994 * A236323 A018923 A264901

Adjacent sequences: A204642 A204643 A204644 * A204646 A204647 A204648

Keyword

nonn

Author

R. H. Hardin, Jan 17 2012

Status

approved