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A211837
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Number of nonnegative integer arrays of length n+4 with new values 0 upwards introduced in order, no three adjacent elements equal, and containing the value n+1.
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1
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33, 77, 157, 289, 492, 788, 1202, 1762, 2499, 3447, 4643, 6127, 7942, 10134, 12752, 15848, 19477, 23697, 28569, 34157, 40528, 47752, 55902, 65054, 75287, 86683, 99327, 113307, 128714, 145642, 164188, 184452, 206537, 230549, 256597, 284793, 315252
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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) = (1/8)*n^4 + (17/12)*n^3 + (51/8)*n^2 + (157/12)*n + 12.
G.f.: x*(33 - 88*x + 102*x^2 - 56*x^3 + 12*x^4) / (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:
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
..1....1....1....1....0....1....1....1....1....1....1....1....1....1....1....1
..1....2....2....2....1....2....2....2....0....2....2....1....2....2....0....0
..2....0....3....3....2....3....0....3....2....1....1....2....3....2....2....1
..3....3....4....1....3....4....3....0....3....3....3....3....4....3....3....2
..4....2....2....1....2....3....4....0....4....4....3....2....3....3....4....3
..2....4....2....4....4....5....1....4....3....3....4....4....4....4....5....4
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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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