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

1,1

Links

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

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

Example

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

Crossrefs

Column 3 of A242322.

Sequence in context: A255244 A261989 A051968 * A200867 A175795 A056777

Adjacent sequences: A242315 A242316 A242317 * A242319 A242320 A242321

Keyword

nonn

Author

R. H. Hardin, May 10 2014

Status

approved