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

Author

R. H. Hardin, May 08 2014

Keywords

• nonn

Comments

Column 3 of A242239.

Examples

			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
		

Links

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

Crossrefs

Cf. A016777, A145112, A242239.

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