A269579 Number of length-n 0..4 arrays with no repeated value differing from the previous repeated value by more than one.

5, 25, 125, 613, 2969, 14239, 67763, 320495, 1508267, 7069055, 33020571, 153815099, 714838023, 3315709471, 15354722091, 71009625019, 328017083175, 1513765237255, 6980228317107, 32165146949139, 148133524803711, 681887792337519

Offset

1,1

Links

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

Formula

Empirical: a(n) = 16*a(n-1) - 93*a(n-2) + 220*a(n-3) - 112*a(n-4) - 192*a(n-5) - 2*a(n-6) + 8*a(n-7).

Empirical g.f.: x*(5 - 55*x + 190*x^2 - 162*x^3 - 154*x^4 + 4*x^5 + 6*x^6) / ((1 - 4*x)*(1 - 4*x - x^2)*(1 - 8*x + 14*x^2 + 8*x^3 - 2*x^4)). - Colin Barker, Jan 24 2019

Example

Some solutions for n=6:
..3. .4. .0. .0. .0. .3. .0. .2. .2. .2. .4. .4. .1. .3. .1. .2
..1. .1. .3. .4. .4. .0. .4. .4. .3. .3. .2. .3. .4. .0. .0. .4
..3. .0. .4. .0. .2. .4. .1. .2. .4. .2. .0. .2. .0. .0. .1. .4
..4. .3. .0. .4. .3. .3. .0. .0. .2. .4. .3. .3. .1. .1. .0. .3
..4. .0. .2. .4. .2. .2. .4. .2. .2. .1. .1. .1. .1. .3. .4. .3
..4. .1. .0. .2. .4. .3. .0. .0. .0. .3. .3. .4. .4. .0. .4. .2

Crossrefs

Column 4 of A269583.

Sequence in context: A228736 A126642 A269615 * A269431 A269686 A269490

Adjacent sequences: A269576 A269577 A269578 * A269580 A269581 A269582

Keyword

nonn

Author

R. H. Hardin, Mar 01 2016

Status

approved