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A204214
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Number of length 6 nonnegative integer arrays starting and ending with 0 with adjacent elements differing by no more than n.
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1
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21, 120, 404, 1025, 2181, 4116, 7120, 11529, 17725, 26136, 37236, 51545, 69629, 92100, 119616, 152881, 192645, 239704, 294900, 359121, 433301, 518420, 615504, 725625, 849901, 989496, 1145620, 1319529, 1512525, 1725956, 1961216, 2219745
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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) = (23/12)*n^4 + (37/6)*n^3 + (91/12)*n^2 + (13/3)*n + 1.
G.f.: x*(21 + 15*x + 14*x^2 - 5*x^3 + 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=5:
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
..4....0....2....2....0....5....0....3....5....0....4....5....4....1....1....3
..1....4....2....2....3....2....2....6....1....5....8...10....8....2....3....5
..4....3....7....1....2....0....3....5....5....4....6...10....3....6....3....6
..2....4....5....3....4....3....0....5....2....5....3....5....4....2....4....3
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....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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