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

1,1

Links

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

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

Example

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

Crossrefs

Column 3 of A269619.

Sequence in context: A180239 A006811 A269685 * A267975 A269489 A259898

Adjacent sequences: A269611 A269612 A269613 * A269615 A269616 A269617

Keyword

nonn

Author

R. H. Hardin, Mar 01 2016

Status

approved