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A269641
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Number of length-4 0..n arrays with no repeated value differing from the previous repeated value by other than plus two or minus 1.
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1
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9, 63, 221, 567, 1209, 2279, 3933, 6351, 9737, 14319, 20349, 28103, 37881, 50007, 64829, 82719, 104073, 129311, 158877, 193239, 232889, 278343, 330141, 388847, 455049, 529359, 612413, 704871, 807417, 920759, 1045629, 1182783, 1333001
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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) = n^4 + 4*n^3 + 3*n^2 + 2*n - 1.
G.f.: x*(3 - x)*(3 + 7*x + x^2 + x^3) / (1 - x)^5.
a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>5.
(End)
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EXAMPLE
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Some solutions for n=3:
..3. .2. .1. .2. .0. .0. .3. .0. .1. .2. .1. .2. .3. .0. .3. .2
..1. .3. .2. .2. .3. .3. .2. .0. .0. .3. .0. .1. .1. .0. .0. .0
..3. .1. .0. .0. .0. .1. .0. .2. .0. .2. .0. .2. .3. .2. .1. .2
..3. .2. .0. .3. .0. .2. .1. .1. .2. .2. .3. .3. .1. .3. .0. .2
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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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