A269464 Number of length-n 0..5 arrays with no repeated value equal to the previous repeated value.

6, 36, 210, 1230, 7170, 41730, 242370, 1405530, 8139570, 47082330, 272068770, 1570817130, 9062549970, 52251339930, 301095703170, 1734220430730, 9984459848370, 57463149169530, 330612722505570, 1901660018436330

Offset

1,1

Links

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

Formula

Empirical: a(n) = 9*a(n-1) - 10*a(n-2) - 50*a(n-3).

Conjectures from Colin Barker, Jan 22 2019: (Start)

G.f.: 6*x*(1 - 3*x - 9*x^2) / ((1 - 5*x)*(1 - 4*x - 10*x^2)).

a(n) = (-84*5^n + (231-57*sqrt(14))*(2-sqrt(14))^n + 3*(2+sqrt(14))^n*(77+19*sqrt(14))) / 350.

(End)

Example

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

Crossrefs

Column 5 of A269467.

Sequence in context: A027910 A075848 A096979 * A123887 A358539 A105492

Adjacent sequences: A269461 A269462 A269463 * A269465 A269466 A269467

Keyword

nonn

Author

R. H. Hardin, Feb 27 2016

Status

approved