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

1,1

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).

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

Example

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

Prog

(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

Crossrefs

Diagonal of A183986.

Sequence in context: A008029 A129080 A138643 * A153364 A124743 A188575

Adjacent sequences: A183974 A183975 A183976 * A183978 A183979 A183980

Keyword

nonn,easy

Author

R. H. Hardin, Jan 08 2011

Extensions

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

Status

approved