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A267227
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Number of length-n 0..3 arrays with no following elements greater than or equal to the first repeated value.
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1
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4, 16, 54, 176, 564, 1790, 5646, 17732, 55512, 173354, 540258, 1680848, 5221740, 16200758, 50204790, 155413724, 480622848, 1484980802, 4584213642, 14140323560, 43583756436, 134239102286, 413179757214, 1270924525556, 3906925144104
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OFFSET
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1,1
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COMMENTS
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LINKS
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FORMULA
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Empirical: a(n) = 9*a(n-1) - 29*a(n-2) + 39*a(n-3) - 18*a(n-4) for n > 5.
G.f.: 2*x*(2 - 10*x + 13*x^2 - x^3 - 3*x^4) / ((1 - x)*(1 - 2*x)*(1 - 3*x)^2).
a(n) = (-9 - 9*2^n + 11*3^(1+n) + 2*3^n*n) / 18 for n>1.
(End)
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EXAMPLE
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Some solutions for n=6:
2 0 1 2 3 2 1 2 3 0 3 1 1 3 2 3
3 1 3 0 0 1 2 3 1 1 2 0 0 3 0 2
2 0 1 2 3 3 3 0 3 0 1 2 3 0 2 3
0 3 3 3 1 2 0 2 1 1 3 1 0 2 3 0
3 3 2 3 1 2 1 3 2 2 2 0 1 1 1 1
0 2 0 0 0 0 2 1 2 3 0 3 3 0 1 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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