A269532 Number of length-n 0..3 arrays with no repeated value differing from the previous repeated value by other than one.

4, 16, 60, 222, 804, 2878, 10192, 35812, 125012, 434110, 1500912, 5170626, 17758812, 60837880, 207965356, 709583398, 2417278172, 8223508510, 27943213944, 94853465148, 321696510276, 1090199408374, 3692112980824, 12496559933794

Offset

1,1

Comments

Column 3 of A269537.

Links

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

Formula

Empirical: a(n) = 7*a(n-1) - 9*a(n-2) - 23*a(n-3) + 31*a(n-4) + 33*a(n-5).

Empirical g.f.: 2*x*(2 - 6*x - 8*x^2 + 19*x^3 + 17*x^4) / ((1 - 3*x)*(1 - 4*x - 3*x^2 + 14*x^3 + 11*x^4)). - Colin Barker, Mar 21 2018

Example

Some solutions for n=9:
..2. .1. .0. .0. .3. .0. .1. .2. .1. .2. .0. .1. .1. .0. .0. .1
..1. .3. .3. .0. .0. .2. .2. .2. .0. .0. .3. .2. .3. .3. .2. .2
..0. .0. .2. .1. .3. .3. .0. .0. .3. .1. .0. .0. .1. .3. .0. .1
..2. .3. .2. .1. .2. .2. .1. .3. .1. .2. .0. .2. .0. .0. .3. .3
..2. .0. .3. .0. .0. .0. .0. .2. .0. .3. .2. .3. .3. .3. .2. .3
..3. .2. .0. .0. .3. .1. .0. .0. .2. .0. .3. .1. .3. .0. .0. .0
..1. .1. .3. .2. .2. .0. .3. .3. .2. .3. .2. .2. .1. .2. .1. .1
..1. .2. .0. .3. .3. .0. .1. .2. .0. .2. .1. .2. .2. .1. .2. .0
..3. .3. .3. .0. .0. .1. .3. .3. .3. .2. .2. .0. .2. .2. .1. .2

Crossrefs

Cf. A269537.

Sequence in context: A268939 A269635 A267928 * A269673 A231896 A128650

Adjacent sequences: A269529 A269530 A269531 * A269533 A269534 A269535

Keyword

nonn

Author

R. H. Hardin, Feb 29 2016

Status

approved