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A201695
Number of n X 3 0..2 arrays with rows and columns lexicographically nondecreasing read forwards and nonincreasing read backwards.
1
3, 18, 116, 395, 989, 2068, 3838, 6541, 10455, 15894, 23208, 32783, 45041, 60440, 79474, 102673, 130603, 163866, 203100, 248979, 302213, 363548, 433766, 513685, 604159, 706078, 820368, 947991, 1089945, 1247264, 1421018, 1612313, 1822291
OFFSET
1,1
COMMENTS
Column 3 of A201700.
LINKS
FORMULA
Empirical: a(n) = (3/2)*n^4 + (4/3)*n^3 - 4*n^2 - (29/6)*n + 9.
Conjectures from Colin Barker, May 23 2018: (Start)
G.f.: x*(3 + 3*x + 56*x^2 - 35*x^3 + 9*x^4) / (1 - x)^5.
a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>5.
(End)
EXAMPLE
Some solutions for n=4:
..1..2..2....0..0..1....0..2..2....0..2..2....1..1..2....0..0..2....0..0..2
..1..2..2....0..2..0....2..0..1....1..1..2....1..2..1....0..2..0....0..1..0
..2..1..2....0..2..0....2..0..1....1..2..0....2..0..1....2..0..0....2..0..0
..2..2..0....2..0..0....2..1..0....2..0..0....2..1..0....2..0..0....2..0..0
CROSSREFS
Cf. A201700.
Sequence in context: A163471 A054122 A213230 * A074566 A291076 A113328
KEYWORD
nonn
AUTHOR
R. H. Hardin, Dec 03 2011
STATUS
approved