A221588 Equals one maps: number of n X 3 binary arrays indicating the locations of corresponding elements equal to exactly one of their king-move neighbors in a random 0..3 n X 3 array.

4, 40, 418, 3760, 31416, 256736, 2075520, 16690688, 133871616, 1072357376, 8584396800, 68697325568, 549667209216, 4397692092416, 35182954414080, 281469306011648, 2251777130889216, 18014307778297856, 144114825151119360

Offset

1,1

Comments

Column 3 of A221590.

Links

R. H. Hardin, Table of n, a(n) for n = 1..174

Formula

Empirical: a(n) = 12*a(n-1) -32*a(n-2) for n>6.

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

G.f.: 2*x*(2 - 4*x + 33*x^2 + 12*x^3 - 164*x^4 + 32*x^5) / ((1 - 4*x)*(1 - 8*x)).

a(n) = 8^n - 169*2^(2*n-7) for n>4.

(End)

Example

Some solutions for n=3:
..0..1..0....0..1..0....1..0..1....1..1..1....0..1..0....0..1..0....1..1..1
..0..1..0....0..0..1....1..0..0....0..1..0....1..0..0....0..0..0....1..1..1
..0..1..1....1..1..1....0..1..0....0..0..1....0..1..1....1..1..1....0..1..1

Crossrefs

Cf. A221590.

Sequence in context: A093141 A220965 A278036 * A114468 A264112 A304447

Adjacent sequences: A221585 A221586 A221587 * A221589 A221590 A221591

Keyword

nonn

Author

R. H. Hardin, Jan 20 2013

Status

approved