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A201445
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Number of n X 2 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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LINKS
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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.
Empirical g.f.: x*(6 + 2*x + 15*x^2 + 7*x^3 + 17*x^4 - 2*x^5 + 9*x^6 - 2*x^7 + x^8 + 3*x^9 + x^11 - x^13) / ((1 - x)^4*(1 + x)^4*(1 + x^2)^3). - Colin Barker, May 23 2018
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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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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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