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A220004
Number of n X 2 arrays of the minimum value of corresponding elements and their horizontal, vertical or antidiagonal neighbors in a random, but sorted with lexicographically nondecreasing rows and nonincreasing columns, 0..3 n X 2 array.
1
4, 7, 20, 58, 141, 308, 637, 1271, 2460, 4624, 8444, 14989, 25888, 43557, 71492, 114640, 179861, 276495, 417049, 618020, 900871, 1293178, 1829967, 2555261, 3523858, 4803362, 6476490, 8643679, 11426018, 14968531, 19443838, 25056222
OFFSET
1,1
COMMENTS
Column 2 of A220010.
LINKS
FORMULA
Empirical: a(n) = (1/40320)*n^8 - (1/10080)*n^7 - (1/2880)*n^6 + (43/720)*n^5 - (2873/5760)*n^4 + (3893/1440)*n^3 - (1121/1120)*n^2 - (10301/840)*n + 18 for n>3.
Conjectures from Colin Barker, Jul 29 2018: (Start)
G.f.: x*(4 - 29*x + 101*x^2 - 206*x^3 + 255*x^4 - 175*x^5 + 43*x^6 + 14*x^7 + 3*x^8 - 15*x^9 + 7*x^10 - x^11) / (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>12.
(End)
EXAMPLE
Some solutions for n=3:
..3..3....0..0....0..0....2..2....2..1....2..2....2..2....1..1....1..1....0..0
..3..3....0..0....0..0....2..1....1..1....2..2....2..2....1..0....1..1....0..0
..3..3....1..1....2..3....1..1....1..1....3..3....2..2....0..0....2..3....1..3
CROSSREFS
Cf. A220010.
Sequence in context: A026570 A111955 A244791 * A367911 A368185 A359603
KEYWORD
nonn
AUTHOR
R. H. Hardin, Dec 03 2012
STATUS
approved