A183981 1/4 the number of (n+1) X 5 binary arrays with all 2 X 2 subblock sums the same.

15, 17, 20, 26, 36, 56, 92, 164, 300, 572, 1100, 2156, 4236, 8396, 16652, 33164, 66060, 131852, 263180, 525836, 1050636, 2100236, 4198412, 8394764, 16785420, 33566732, 67125260, 134242316, 268468236, 536920076, 1073807372, 2147581964, 4295098380

Offset

1,1

Comments

Column 4 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 08 2018: (Start)

G.f.: x*(15 - 28*x - 31*x^2 + 56*x^3) / ((1 - x)*(1 - 2*x)*(1 - 2*x^2)).

a(n) = 3*2^(n/2-1) + 2^(n-1) + 12 for n even.

a(n) = 2^(n-1) + 2^((n+1)/2) + 12 for n odd.

(End)

Example

Some solutions for 7 X 5:
..0..1..0..1..0....0..0..0..0..1....0..1..0..1..0....0..1..0..1..0
..1..1..1..1..1....1..0..1..0..0....0..1..0..1..0....0..0..0..0..0
..0..1..0..1..0....0..0..0..0..1....1..0..1..0..1....1..0..1..0..1
..1..1..1..1..1....1..0..1..0..0....1..0..1..0..1....0..0..0..0..0
..1..0..1..0..1....0..0..0..0..1....0..1..0..1..0....1..0..1..0..1
..1..1..1..1..1....1..0..1..0..0....0..1..0..1..0....0..0..0..0..0
..1..0..1..0..1....0..0..0..0..1....1..0..1..0..1....1..0..1..0..1

Crossrefs

Cf. A183986.

Sequence in context: A043704 A329177 A074748 * A155111 A124334 A002155

Adjacent sequences: A183978 A183979 A183980 * A183982 A183983 A183984

Keyword

nonn

Author

R. H. Hardin, Jan 08 2011

Status

approved