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A201445
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Number of nX2 0..3 arrays with every row and column nondecreasing rightwards and downwards, and the number of instances of each value within one of each other
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1
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6, 2, 21, 9, 56, 13, 110, 32, 198, 41, 315, 78, 480, 94, 684, 155, 950, 180, 1265, 271, 1656, 307, 2106, 434, 2646, 483, 3255, 652, 3968, 716, 4760, 933, 5670, 1014, 6669, 1285, 7800, 1385, 9030, 1716, 10406, 1837, 11891, 2234, 13536, 2378, 15300, 2847
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OFFSET
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1,1
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COMMENTS
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Column 2 of A201451
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LINKS
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R. H. Hardin, Table of n, a(n) for n = 1..210
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FORMULA
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Empirical: a(n) = a(n-2) +3*a(n-4) -3*a(n-6) -3*a(n-8) +3*a(n-10) +a(n-12) -a(n-14)
Subsequences for n modulo 4 = 1,2,3,0
p=(n+3)/4: a(n) = 8*p^3 - 2*p^2
q=(n+2)/4: a(n) = (4/3)*q^3 + (1/2)*q^2 + (1/6)*q
r=(n+1)/4: a(n) = 8*r^3 + 10*r^2 + 3*r
s=(n+0)/4: a(n) = (4/3)*s^3 + (7/2)*s^2 + (19/6)*s + 1
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EXAMPLE
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Some solutions for n=10
..0..0....0..0....0..1....0..1....0..2....0..0....0..0....0..0....0..1....0..0
..0..1....0..1....0..1....0..1....0..2....0..1....0..1....0..0....0..1....0..1
..0..2....0..1....0..2....0..2....0..2....0..1....0..2....0..1....0..1....0..2
..0..2....0..2....0..2....0..2....0..2....0..1....0..2....1..1....0..2....0..2
..1..2....1..2....0..2....0..2....0..2....1..1....1..2....1..1....0..2....1..2
..1..2....1..2....1..2....1..3....1..3....2..2....1..3....2..2....1..2....1..2
..1..2....1..2....1..2....1..3....1..3....2..3....1..3....2..3....1..3....1..3
..1..3....2..3....1..3....1..3....1..3....2..3....1..3....2..3....2..3....1..3
..3..3....3..3....3..3....2..3....1..3....2..3....2..3....2..3....2..3....2..3
..3..3....3..3....3..3....2..3....1..3....3..3....2..3....3..3....3..3....3..3
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CROSSREFS
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Sequence in context: A055943 A213503 A169632 * A090033 A036173 A142707
Adjacent sequences: A201442 A201443 A201444 * A201446 A201447 A201448
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KEYWORD
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nonn
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AUTHOR
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R. H. Hardin Dec 01 2011
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STATUS
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approved
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