A242318 Number of length n+3+2 0..3 arrays with every value 0..3 appearing at least once in every consecutive 3+3 elements, and new values 0..3 introduced in order.

65, 185, 503, 1316, 3398, 8801, 23069, 60197, 156887, 408962, 1066514, 2781611, 7253453, 18914369, 49323167, 128621684, 335409314, 874649537, 2280834353, 5947765493, 15510073823, 40445831522, 105471145814, 275038567523

Offset: 1

Author

R. H. Hardin, May 10 2014

Keywords

• nonn

Examples

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

Links

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

Crossrefs

Column 3 of A242322.

Formula

Empirical: a(n) = a(n-1) + 2*a(n-2) + 3*a(n-3) + 5*a(n-4) + 6*a(n-5) - a(n-6) - a(n-7) - a(n-9) - a(n-10).

Empirical g.f.: x*(65 + 120*x + 188*x^2 + 248*x^3 + 196*x^4 - 53*x^5 - 36*x^6 - 16*x^7 - 49*x^8 - 35*x^9) / (1 - x - 2*x^2 - 3*x^3 - 5*x^4 - 6*x^5 + x^6 + x^7 + x^9 + x^10). - Colin Barker, Nov 01 2018