A267905 Number of n X 1 0..2 arrays with every repeated value in every row unequal to the previous repeated value, and in every column equal to the previous repeated value, and new values introduced in row-major sequential order.

1, 2, 5, 13, 34, 88, 225, 569, 1426, 3548, 8777, 21613, 53026, 129712, 316545, 770993, 1874914, 4553588, 11047625, 26779909, 64869586, 157043368, 380004897, 919150313, 2222499826, 5372538572, 12984354185, 31374801373, 75801065794

Offset

1,2

Links

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

Formula

Empirical: a(n) = 5*a(n-1) -7*a(n-2) +a(n-3) +2*a(n-4).

Conjectures from Colin Barker, Jan 11 2019: (Start)

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

a(n) = ((1-sqrt(2))^(1+n) + (1+sqrt(2))^(1+n) - 2*(2^n-1)) / 4.

(End)

Example

Some solutions for n=8:
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
..0....1....1....1....1....1....1....1....1....1....1....1....1....1....1....0
..1....2....2....0....2....2....2....1....2....0....2....0....2....0....2....0
..2....2....2....0....1....1....1....1....0....1....0....1....1....0....0....1
..0....1....2....2....2....1....2....2....0....1....0....2....0....0....0....2
..1....0....2....0....1....1....1....1....1....1....0....0....2....2....0....1
..2....2....2....0....2....1....2....0....0....0....1....1....2....0....0....0
..1....2....2....1....1....1....2....2....2....1....0....1....2....0....2....0

Crossrefs

Column 1 of A267911.

Sequence in context: A371426 A027931 A218481 * A209230 A103142 A112844

Adjacent sequences: A267902 A267903 A267904 * A267906 A267907 A267908

Keyword

nonn

Author

R. H. Hardin, Jan 22 2016

Status

approved