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A219465
Number of n X 2 arrays of the minimum value of corresponding elements and their horizontal or antidiagonal neighbors in a random, but sorted with lexicographically nondecreasing rows and columns, 0..3 n X 2 array.
1
4, 23, 82, 239, 619, 1471, 3259, 6800, 13464, 25453, 46178, 80755, 136643, 224449, 358927, 560200, 855236, 1279611, 1879594, 2714591, 3859987, 5410427, 7483579, 10224424, 13810120, 18455489, 24419178, 32010547, 41597339, 53614189, 68572031
OFFSET
1,1
COMMENTS
Column 2 of A219471.
LINKS
FORMULA
Empirical: a(n) = (1/20160)*n^8 + (1/1260)*n^7 + (1/480)*n^6 + (4/45)*n^5 - (11/960)*n^4 + (277/180)*n^3 + (7607/5040)*n^2 + (61/70)*n.
Conjectures from Colin Barker, Jul 26 2018: (Start)
G.f.: x*(4 - 13*x + 19*x^2 - 7*x^3 - 8*x^4 + 10*x^5 - 2*x^6 - x^7) / (1 - x)^9.
a(n) = 9*a(n-1) - 36*a(n-2) + 84*a(n-3) - 126*a(n-4) + 126*a(n-5) - 84*a(n-6) + 36*a(n-7) - 9*a(n-8) + a(n-9) for n>9.
(End)
EXAMPLE
Some solutions for n=3:
..2..2....0..0....1..1....1..1....2..2....1..1....1..1....0..0....1..1....1..1
..0..0....1..1....0..0....1..1....0..0....1..1....1..1....0..1....1..1....2..2
..0..1....3..3....0..3....0..0....0..3....1..3....1..2....0..0....3..3....2..3
CROSSREFS
Cf. A219471.
Sequence in context: A304305 A316204 A305771 * A317120 A220647 A014585
KEYWORD
nonn
AUTHOR
R. H. Hardin, Nov 20 2012
STATUS
approved