A183977 1/4 the number of (n+1) X (n+1) binary arrays with all 2 X 2 subblock sums the same.

4, 8, 14, 26, 46, 86, 158, 302, 574, 1118, 2174, 4286, 8446, 16766, 33278, 66302, 132094, 263678, 526334, 1051646, 2101246, 4200446, 8396798, 16789502, 33570814, 67133438, 134250494, 268484606, 536936446, 1073840126, 2147614718, 4295163902

Offset: 1

Author

R. H. Hardin, Jan 08 2011

Keywords

• nonn
• easy

Examples

			Some solutions for 5X5
..1..0..1..0..1....0..1..0..1..0....1..1..1..1..1....0..1..1..0..1
..1..0..1..0..1....1..0..1..0..1....0..1..0..1..0....1..0..0..1..0
..0..1..0..1..0....1..0..1..0..1....1..1..1..1..1....0..1..1..0..1
..1..0..1..0..1....1..0..1..0..1....1..0..1..0..1....1..0..0..1..0
..0..1..0..1..0....1..0..1..0..1....1..1..1..1..1....0..1..1..0..1
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (3,0,-6,4).

Crossrefs

Diagonal of A183986.

Programs

PARI

Vec(2*(2 - 2*x - 5*x^2 + 4*x^3)/((1 - x)*(1 - 2*x)*(1 - 2*x^2)) + O(x^32)) \\ Andrew Howroyd, Mar 09 2024

Formula

From Andrew Howroyd, Mar 09 2024: (Start)

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

G.f.: 2*x*(2 - 2*x - 5*x^2 + 4*x^3)/((1 - x)*(1 - 2*x)*(1 - 2*x^2)). (End)

E.g.f.: 3*cosh(sqrt(2)*x) + cosh(2*x) - 2*cosh(x) - 2 - 2*sinh(x) + sinh(2*x) + 2*sqrt(2)*sinh(sqrt(2)*x). - Stefano Spezia, Oct 16 2024

Extensions

a(19) onwards from Andrew Howroyd, Mar 09 2024