A269651 Number of length-n 0..3 arrays with no adjacent pair x,x+1 repeated.

4, 16, 64, 253, 988, 3816, 14596, 55344, 208196, 777582, 2885120, 10640607, 39027196, 142415244, 517252820, 1870499543, 6736838192, 24172420350, 86428990624, 308016010824, 1094338584760, 3876828265788, 13696906252336

Offset: 1

Author

R. H. Hardin, Mar 02 2016

Keywords

• nonn

Comments

Column 3 of A269656.

Examples

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

Links

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

Crossrefs

Cf. A269656.

Formula

Empirical: a(n) = 16*a(n-1) -108*a(n-2) +408*a(n-3) -986*a(n-4) +1704*a(n-5) -2312*a(n-6) +2560*a(n-7) -2355*a(n-8) +1832*a(n-9) -1208*a(n-10) +672*a(n-11) -314*a(n-12) +120*a(n-13) -36*a(n-14) +8*a(n-15) -a(n-16)