A269687 Number of length-n 0..5 arrays with no repeated value differing from the previous repeated value by plus or minus one modulo 5+1.

6, 36, 216, 1284, 7584, 44556, 260616, 1518804, 8823984, 51132636, 295646616, 1706201124, 9830779584, 56564639916, 325076005416, 1866287024244, 10704981330384, 61356265686396, 351432308441016, 2011741878388164

Offset

1,1

Links

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

Formula

Empirical: a(n) = 10*a(n-1) - 21*a(n-2) - 20*a(n-3).

Conjectures from Colin Barker, Jan 27 2019: (Start)

G.f.: 6*x*(1 - 4*x - 3*x^2) / ((1 - 5*x)*(1 - 5*x - 4*x^2)).

a(n) = (3/205)*2^(-2-n)*(-41*2^(2+n)*5^n-5*(5-sqrt(41))^n*(-41+7*sqrt(41)) + 5*(5+sqrt(41))^n*(41+7*sqrt(41))).

(End)

Example

Some solutions for n=6:
..2. .2. .2. .5. .2. .0. .4. .4. .4. .0. .1. .5. .3. .1. .3. .4
..3. .2. .3. .2. .1. .4. .1. .5. .5. .3. .4. .5. .5. .4. .5. .3
..4. .1. .1. .0. .2. .5. .1. .2. .2. .5. .0. .2. .1. .0. .2. .4
..5. .5. .5. .4. .1. .4. .2. .4. .4. .2. .5. .4. .1. .4. .1. .0
..5. .1. .2. .2. .5. .5. .1. .1. .5. .1. .3. .3. .3. .0. .3. .5
..4. .5. .4. .4. .5. .0. .1. .1. .4. .5. .2. .1. .2. .1. .2. .4

Crossrefs

Column 5 of A269690.

Sequence in context: A269616 A269580 A269432 * A269491 A269773 A269653

Adjacent sequences: A269684 A269685 A269686 * A269688 A269689 A269690

Keyword

nonn

Author

R. H. Hardin, Mar 03 2016

Status

approved