A269531 Number of length-n 0..2 arrays with no repeated value differing from the previous repeated value by other than one.

3, 9, 24, 64, 164, 418, 1048, 2614, 6468, 15942, 39120, 95734, 233660, 569230, 1384408, 3362686, 8158932, 19778982, 47913504, 115999462, 280698860, 678970558, 1641785704, 3968834446, 9592037508, 23178077334, 55998523824, 135275792374

Offset

1,1

Links

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

Formula

Empirical: a(n) = 4*a(n-1) - a(n-2) - 10*a(n-3) + 6*a(n-4) + 4*a(n-5).

Empirical g.f.: x*(3 - 3*x - 9*x^2 + 7*x^3 + 4*x^4) / ((1 - 2*x)*(1 - 2*x - x^2)*(1 - 2*x^2)). - Colin Barker, Jan 23 2019

Example

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

Crossrefs

Column 2 of A269537.

Sequence in context: A166290 A097134 A123892 * A064831 A153582 A269461

Adjacent sequences: A269528 A269529 A269530 * A269532 A269533 A269534

Keyword

nonn

Author

R. H. Hardin, Feb 29 2016

Status

approved