A208138 Number of n X 4 0..1 arrays avoiding 0 0 1 and 0 1 1 horizontally and 0 0 1 and 1 0 1 vertically.

9, 81, 324, 900, 2025, 3969, 7056, 11664, 18225, 27225, 39204, 54756, 74529, 99225, 129600, 166464, 210681, 263169, 324900, 396900, 480249, 576081, 685584, 810000, 950625, 1108809, 1285956, 1483524, 1703025, 1946025, 2214144, 2509056, 2832489

Offset

1,1

Comments

Column 4 of A208142.

Links

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

Formula

Empirical: a(n) = (9/4)*n^4 + (9/2)*n^3 + (9/4)*n^2.

Conjectures from Colin Barker, Jun 28 2018: (Start)

G.f.: 9*x*(1 + 4*x + x^2) / (1 - x)^5.

a(n) = 9*(n^2*(1+n)^2) / 4.

(End)

Example

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

Crossrefs

Cf. A208142.

Sequence in context: A207962 A207501 A207438 * A207444 A207428 A208370

Adjacent sequences: A208135 A208136 A208137 * A208139 A208140 A208141

Keyword

nonn

Author

R. H. Hardin, Feb 23 2012

Status

approved