A242234 Number of length n+3+1 0..3 arrays with every value 0..3 appearing at least once in every consecutive 3+2 elements, and new values 0..3 introduced in order.

10, 22, 43, 82, 157, 304, 586, 1129, 2176, 4195, 8086, 15586, 30043, 57910, 111625, 215164, 414742, 799441, 1540972, 2970319, 5725474, 11036206, 21272971, 41004970, 79039621, 152353768, 293671330, 566069689, 1091134408, 2103229195, 4054104622

Offset

1,1

Comments

Column 3 of A242239.

Links

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

Formula

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

Conjecture: a(n) = 9*A145112(n-1) + A016777(n-1). - R. J. Mathar, Aug 16 2017

Empirical g.f.: x*(10 + 12*x + 11*x^2 + 7*x^3) / (1 - x - x^2 - x^3 - x^4). - Colin Barker, Mar 19 2018

Example

Some solutions for n=5:
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
..1....1....1....1....1....0....1....1....1....1....0....1....1....1....1....1
..1....2....2....2....2....1....2....0....1....0....1....2....2....2....2....0
..2....1....3....3....0....2....3....2....2....2....2....0....0....3....1....2
..3....3....0....0....3....3....0....3....3....3....3....3....3....0....3....3
..0....0....1....3....1....0....2....0....0....0....0....1....2....1....0....1
..2....2....2....1....2....0....1....1....1....1....1....2....1....2....2....3
..1....1....3....2....2....1....2....1....2....2....1....0....0....3....0....0
..1....3....0....2....0....2....3....2....1....3....2....2....0....3....1....2

Crossrefs

Cf. A016777, A145112, A242239.

Sequence in context: A014367 A063710 A157917 * A104867 A179877 A216048

Adjacent sequences: A242231 A242232 A242233 * A242235 A242236 A242237

Keyword

nonn

Author

R. H. Hardin, May 08 2014

Status

approved