A269489 Number of length-n 0..3 arrays with no repeated value differing from the previous repeated value by one.

4, 16, 64, 250, 964, 3680, 13946, 52562, 197288, 738190, 2755492, 10266910, 38201266, 141989786, 527337242, 1957297844, 7261528508, 26930981728, 99854569606, 370173077224, 1372098494764, 5085413836406, 18846930103274

Offset

1,1

Comments

Column 3 of A269494.

Links

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

Formula

Empirical: a(n) = 9*a(n-1) - 24*a(n-2) + 9*a(n-3) + 26*a(n-4) + 3*a(n-5).

Empirical g.f.: 2*x*(2 - 10*x + 8*x^2 + 11*x^3 + x^4) / ((1 - 3*x)*(1 - 6*x + 6*x^2 + 9*x^3 + x^4)). - Colin Barker, Mar 21 2018

Example

Some solutions for n=6:
..1. .2. .2. .0. .0. .3. .0. .0. .3. .2. .1. .2. .3. .3. .2. .0
..2. .2. .1. .3. .1. .3. .2. .2. .3. .2. .0. .1. .2. .2. .0. .0
..2. .0. .2. .3. .0. .3. .1. .1. .2. .2. .3. .1. .1. .1. .1. .2
..2. .3. .3. .1. .1. .2. .3. .3. .3. .1. .1. .0. .3. .0. .2. .3
..0. .2. .0. .2. .3. .3. .1. .1. .1. .2. .2. .1. .1. .2. .0. .0
..1. .3. .0. .3. .0. .2. .2. .3. .3. .3. .2. .2. .0. .2. .3. .3

Crossrefs

Cf. A269494.

Sequence in context: A269685 A269614 A267975 * A259898 A307945 A370143

Adjacent sequences: A269486 A269487 A269488 * A269490 A269491 A269492

Keyword

nonn

Author

R. H. Hardin, Feb 28 2016

Status

approved