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

Index entries for linear recurrences with constant coefficients, signature (3, 0, -6, 4).

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)

The above empirical formula is correct. See note from Andrew Howroyd in A183986.

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