A269772 Number of length-n 0..4 arrays with every repeated value unequal to the previous repeated value plus one mod 4+1.

5, 25, 125, 620, 3060, 15040, 73680, 360000, 1755200, 8542720, 41519360, 201559040, 977556480, 4737433600, 22943846400, 111060664320, 537360220160, 2599052247040, 12567124705280, 60750607155200, 293614524825600

Offset

1,1

Links

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

Formula

Empirical: a(n) = 8*a(n-1) - 12*a(n-2) - 16*a(n-3).

Empirical g.f.: 5*x*(1 - 3*x - 3*x^2) / ((1 - 4*x)*(1 - 4*x - 4*x^2)). - Colin Barker, Jan 29 2019

Example

Some solutions for n=7:
..2. .2. .4. .4. .3. .2. .1. .4. .4. .1. .0. .3. .4. .4. .0. .3
..4. .0. .2. .1. .1. .2. .2. .0. .1. .2. .4. .1. .4. .2. .3. .3
..1. .1. .2. .3. .0. .0. .1. .2. .2. .0. .3. .0. .4. .4. .1. .1
..3. .0. .2. .3. .3. .2. .3. .1. .1. .4. .4. .3. .4. .3. .1. .2
..2. .1. .1. .3. .0. .2. .2. .4. .3. .3. .1. .4. .2. .2. .0. .4
..3. .4. .4. .2. .2. .4. .0. .0. .2. .1. .0. .4. .4. .1. .4. .0
..0. .1. .1. .2. .2. .0. .3. .3. .2. .0. .2. .1. .4. .3. .0. .4

Crossrefs

Column 4 of A269776.

Sequence in context: A269686 A269490 A370144 * A269652 A163844 A250357

Adjacent sequences: A269769 A269770 A269771 * A269773 A269774 A269775

Keyword

nonn

Author

R. H. Hardin, Mar 04 2016

Status

approved