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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.
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
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
KEYWORD
nonn
AUTHOR
R. H. Hardin, Mar 03 2016
STATUS
approved