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A269464
Number of length-n 0..5 arrays with no repeated value equal to the previous repeated value.
1
6, 36, 210, 1230, 7170, 41730, 242370, 1405530, 8139570, 47082330, 272068770, 1570817130, 9062549970, 52251339930, 301095703170, 1734220430730, 9984459848370, 57463149169530, 330612722505570, 1901660018436330
OFFSET
1,1
LINKS
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
KEYWORD
nonn
AUTHOR
R. H. Hardin, Feb 27 2016
STATUS
approved