A268941 Number of length-n 0..5 arrays with no repeated value unequal to the previous repeated value plus one mod 5+1.

6, 36, 210, 1206, 6834, 38322, 213042, 1175850, 6450402, 35200458, 191222994, 1034688474, 5579060610, 29989217034, 160755450546, 859578198138, 4585950964578, 24416800390890, 129760544069778, 688431162218202

Offset

1,1

Links

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

Formula

Empirical: a(n) = 9*a(n-1) - 14*a(n-2) - 30*a(n-3).

Conjectures from Colin Barker, Jan 17 2019: (Start)

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

a(n) = (-12*5^(1+n) + (35-11*sqrt(10))*(2-sqrt(10))^n + (2+sqrt(10))^n*(35+11*sqrt(10))) / 10.

(End)

Example

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

Crossrefs

Column 5 of A268944.

Sequence in context: A354229 A354231 A014336 * A269637 A269534 A269675

Adjacent sequences: A268938 A268939 A268940 * A268942 A268943 A268944

Keyword

nonn

Author

R. H. Hardin, Feb 16 2016

Status

approved