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A269462
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Number of length-n 0..3 arrays with no repeated value equal to the previous repeated value.
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1
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4, 16, 60, 228, 852, 3180, 11796, 43644, 160980, 592572, 2177268, 7988700, 29277204, 107195196, 392179380, 1433907228, 5240022612, 19140884220, 69894090996, 255150047964, 931214323860, 3397977981372, 12397189043508, 45224087388060
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OFFSET
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1,1
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LINKS
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FORMULA
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Empirical: a(n) = 5*a(n-1) - 18*a(n-3).
G.f.: 4*x*(1 - x - 5*x^2) / ((1 - 3*x)*(1 - 2*x - 6*x^2)).
a(n) = (-28*3^n + (49-17*sqrt(7))*(1-sqrt(7))^n + (1+sqrt(7))^n*(49+17*sqrt(7))) / 63.
(End)
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EXAMPLE
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Some solutions for n=9:
..1. .1. .2. .2. .0. .0. .1. .2. .1. .2. .0. .2. .1. .1. .1. .0
..0. .1. .1. .1. .3. .2. .3. .0. .2. .1. .1. .1. .3. .2. .2. .1
..1. .2. .2. .3. .1. .0. .2. .0. .1. .0. .3. .2. .3. .0. .2. .0
..0. .1. .3. .0. .3. .0. .1. .2. .0. .0. .0. .1. .0. .3. .1. .1
..1. .2. .0. .1. .1. .1. .0. .2. .3. .1. .2. .1. .3. .3. .1. .0
..2. .3. .3. .2. .3. .2. .1. .0. .1. .3. .1. .3. .2. .1. .0. .0
..0. .0. .0. .2. .1. .3. .2. .0. .3. .2. .1. .1. .3. .3. .3. .1
..2. .0. .1. .0. .3. .0. .0. .2. .3. .0. .2. .0. .1. .2. .0. .1
..2. .3. .0. .0. .2. .2. .3. .2. .2. .2. .2. .0. .0. .2. .0. .0
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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