A269614 Number of length-n 0..3 arrays with no repeated value differing from the previous repeated value by other than plus two, zero or minus 1.

4, 16, 64, 249, 954, 3611, 13544, 50442, 186822, 688899, 2531406, 9275757, 33912330, 123759252, 450985950, 1641487455, 5969001906, 21688869249, 78760649178, 285872602590, 1037218320720, 3762161399673, 13642773106086, 49463937282915

Offset: 1

Author

R. H. Hardin, Mar 01 2016

Keywords

• nonn

Examples

			Some solutions for n=8:
..0. .3. .2. .3. .1. .0. .0. .0. .2. .2. .2. .3. .2. .2. .2. .3
..3. .3. .1. .3. .3. .2. .2. .2. .0. .3. .1. .1. .1. .3. .2. .0
..3. .0. .3. .2. .2. .1. .0. .3. .1. .3. .3. .3. .2. .0. .2. .0
..2. .3. .2. .2. .1. .3. .0. .3. .0. .1. .2. .2. .1. .0. .1. .2
..3. .2. .3. .2. .0. .2. .1. .0. .1. .0. .0. .3. .3. .1. .3. .0
..1. .2. .3. .1. .0. .3. .2. .3. .3. .3. .0. .2. .1. .2. .1. .2
..0. .1. .0. .3. .3. .3. .0. .2. .0. .3. .2. .3. .2. .0. .0. .0
..3. .0. .2. .0. .1. .1. .2. .3. .2. .1. .3. .3. .1. .0. .3. .1
		

Links

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

Crossrefs

Column 3 of A269619.

Formula

Empirical: a(n) = 12*a(n-1) - 51*a(n-2) + 81*a(n-3) - 3*a(n-4) - 63*a(n-5) - 24*a(n-6) - 9*a(n-7).

Empirical g.f.: x*(4 - 32*x + 76*x^2 - 27*x^3 - 54*x^4 - 22*x^5 - 7*x^6) / ((1 - 3*x)*(1 - 9*x + 24*x^2 - 9*x^3 - 24*x^4 - 9*x^5 - 3*x^6)). - Colin Barker, Jan 25 2019