A183983 1/4 the number of (n+1) X 7 binary arrays with all 2 X 2 subblock sums the same.

45, 47, 50, 56, 66, 86, 122, 194, 330, 602, 1130, 2186, 4266, 8426, 16682, 33194, 66090, 131882, 263210, 525866, 1050666, 2100266, 4198442, 8394794, 16785450, 33566762, 67125290, 134242346, 268468266, 536920106, 1073807402, 2147581994, 4295098410

Offset

1,1

Comments

Column 6 of A183986.

Links

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

Formula

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

G.f.: x*(45 - 88*x - 91*x^2 + 176*x^3) / ((1 - x)*(1 - 2*x)*(1 - 2*x^2)).

a(n) = 3*2^(n/2-1) + 2^(n-1) + 42 for n even.

a(n) = 2^(n-1) + 2^((n+1)/2) + 42 for n odd.

a(n) = 3*a(n-1) - 6*a(n-3) + 4*a(n-4) for n>4.

(End)

Example

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

Crossrefs

Cf. A183986.

Sequence in context: A252721 A042011 A031064 * A116334 A291788 A291787

Adjacent sequences: A183980 A183981 A183982 * A183984 A183985 A183986

Keyword

nonn

Author

R. H. Hardin, Jan 08 2011

Status

approved