A204646 Number of (n+1) X 4 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.

28, 56, 104, 178, 284, 434, 637, 908, 1259, 1708, 2270, 2966, 3814, 4838, 6059, 7504, 9197, 11168, 13444, 16058, 19040, 22426, 26249, 30548, 35359, 40724, 46682, 53278, 60554, 68558, 77335, 86936, 97409, 108808, 121184, 134594, 149092, 164738, 181589

Offset

1,1

Comments

Column 3 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) for n>7.

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

G.f.: x*(28 - 56*x + 20*x^2 + 42*x^3 - 48*x^4 + 20*x^5 - 3*x^6) / ((1 - x)^5*(1 + x)).

a(n) = (256 + 400*n + 144*n^2 + 16*n^3 + 2*n^4)/32 for n>1 and even.

a(n) = (238 + 400*n + 144*n^2 + 16*n^3 + 2*n^4)/32 for n>1 and odd.

(End)

Example

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

Crossrefs

Cf. A204651.

Sequence in context: A119168 A040756 A135628 * A211491 A270297 A068576

Adjacent sequences: A204643 A204644 A204645 * A204647 A204648 A204649

Keyword

nonn

Author

R. H. Hardin, Jan 17 2012

Status

approved