

A220147


Number of n X 2 arrays of the minimum value of corresponding elements and their horizontal or diagonal neighbors in a random, but sorted with lexicographically nondecreasing rows and nonincreasing columns, 0..2 n X 2 array.


1



3, 11, 26, 52, 95, 163, 266, 416, 627, 915, 1298, 1796, 2431, 3227, 4210, 5408, 6851, 8571, 10602, 12980, 15743, 18931, 22586, 26752, 31475, 36803, 42786, 49476, 56927, 65195, 74338, 84416, 95491, 107627, 120890, 135348, 151071, 168131, 186602
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OFFSET

1,1


COMMENTS



LINKS



FORMULA

Empirical: a(n) = (1/12)*n^4  (1/6)*n^3 + (29/12)*n^2 + (2/3)*n.
G.f.: x*(3  4*x + x^2 + 2*x^3) / (1  x)^5.
a(n) = 5*a(n1)  10*a(n2) + 10*a(n3)  5*a(n4) + a(n5) for n>5.
(End)


EXAMPLE

Some solutions for n=3:
..0..0....0..0....1..1....0..1....1..1....0..0....1..1....2..2....0..0....0..0
..0..0....0..0....2..1....0..0....0..1....2..2....2..2....2..2....0..0....1..0
..2..2....0..0....2..2....2..2....0..0....2..2....2..2....2..2....1..1....2..2


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



