A251328 Number of (n+1) X (1+1) 0..2 arrays with every 2 X 2 subblock summing to 2 4 or 6.

39, 171, 753, 3333, 14823, 66219, 297057, 1337733, 6045495, 27408747, 124625745, 568146309, 2596130823, 11887635627, 54533628609, 250576195845, 1153020767319, 5312272049259, 24501992068785, 113120150702085, 522688044131367

Offset

1,1

Links

R. H. Hardin, Table of n, a(n) for n = 1..210

Formula

Empirical: a(n) = 8*a(n-1) - 13*a(n-2) - 12*a(n-3).

Conjectures from Colin Barker, Nov 29 2018: (Start)

G.f.: 3*x*(13 - 47*x - 36*x^2) / ((1 - 4*x)*(1 - 4*x - 3*x^2)).

a(n) = (7*2^(3+2*n) + (35-13*sqrt(7))*(2-sqrt(7))^n + (2+sqrt(7))^n*(35+13*sqrt(7))) / 14.

(End)

Example

Some solutions for n=4:
..2..0....2..0....2..1....0..1....1..2....1..1....2..0....2..2....2..0....0..0
..1..1....0..2....2..1....2..1....0..1....1..1....1..1....0..2....1..1....2..0
..1..1....0..0....1..0....0..1....1..0....1..1....0..2....2..0....1..1....2..2
..0..0....1..1....1..2....1..2....2..1....0..2....0..2....0..2....0..0....1..1
..2..2....0..2....1..2....1..2....1..2....0..2....2..2....2..0....1..1....0..0

Crossrefs

Column 1 of A251335.

Sequence in context: A158598 A105838 A251335 * A235981 A235974 A258095

Adjacent sequences: A251325 A251326 A251327 * A251329 A251330 A251331

Keyword

nonn

Author

R. H. Hardin, Dec 01 2014

Status

approved