A183984 1/4 the number of (n+1) X 8 binary arrays with all 2 X 2 subblock sums the same.

81, 83, 86, 92, 102, 122, 158, 230, 366, 638, 1166, 2222, 4302, 8462, 16718, 33230, 66126, 131918, 263246, 525902, 1050702, 2100302, 4198478, 8394830, 16785486, 33566798, 67125326, 134242382, 268468302, 536920142, 1073807438, 2147582030

Offset

1,1

Comments

Column 7 of A183986.

Links

R. H. Hardin, Table of n, a(n) for n = 1..200

Formula

Empirical: a(n) = 3*a(n-1) - 6*a(n-3) + 4*a(n-4).

Conjectures from Colin Barker, Apr 09 2018: (Start)

G.f.: x*(81 - 160*x - 163*x^2 + 320*x^3) / ((1 - x)*(1 - 2*x)*(1 - 2*x^2)).

a(n) = 3*2^(n/2-1) + 2^(n-1) + 78 for n even.

a(n) = 2^(n-1) + 2^((n+1)/2) + 78 for n odd.

(End)

Example

Some solutions for 5 X 8.
..0..0..1..1..1..1..0..1....1..1..0..1..1..0..1..1....1..0..1..0..1..0..1..0
..1..1..0..0..0..0..1..0....0..0..1..0..0..1..0..0....1..1..1..1..1..1..1..1
..0..0..1..1..1..1..0..1....1..1..0..1..1..0..1..1....0..1..0..1..0..1..0..1
..1..1..0..0..0..0..1..0....0..0..1..0..0..1..0..0....1..1..1..1..1..1..1..1
..0..0..1..1..1..1..0..1....1..1..0..1..1..0..1..1....1..0..1..0..1..0..1..0

Crossrefs

Cf. A183986.

Sequence in context: A075691 A055390 A186472 * A089784 A186464 A345477

Adjacent sequences: A183981 A183982 A183983 * A183985 A183986 A183987

Keyword

nonn

Author

R. H. Hardin, Jan 08 2011

Status

approved