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A201975
Number of n X 2 0..3 arrays with rows and columns lexicographically nondecreasing read forwards and nonincreasing read backwards.
1
4, 30, 72, 131, 208, 304, 420, 557, 716, 898, 1104, 1335, 1592, 1876, 2188, 2529, 2900, 3302, 3736, 4203, 4704, 5240, 5812, 6421, 7068, 7754, 8480, 9247, 10056, 10908, 11804, 12745, 13732, 14766, 15848, 16979, 18160, 19392, 20676, 22013, 23404, 24850
OFFSET
1,1
COMMENTS
Column 2 of A201981.
LINKS
FORMULA
Empirical: a(n) = (1/6)*n^3 + 7*n^2 + (23/6)*n - 7.
Conjectures from Colin Barker, May 25 2018: (Start)
G.f.: x*(4 + 14*x - 24*x^2 + 7*x^3) / (1 - x)^4.
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>4.
(End)
EXAMPLE
Some solutions for n=9.
..0..3....1..3....0..3....0..3....1..3....0..3....0..3....1..2....0..3....0..1
..0..3....1..3....0..3....0..3....2..2....0..3....1..2....3..1....0..3....3..0
..1..2....1..3....0..3....0..3....2..2....0..3....1..2....3..1....1..2....3..0
..1..2....1..3....0..3....0..3....2..2....0..3....1..2....3..1....2..1....3..0
..1..2....1..3....2..0....0..3....2..2....2..1....1..2....3..1....2..1....3..0
..2..0....1..3....2..0....1..2....2..2....2..1....1..2....3..1....2..1....3..0
..2..0....2..2....2..0....1..2....2..2....2..1....1..2....3..1....3..0....3..0
..2..0....3..1....2..0....1..2....3..0....2..1....3..1....3..1....3..0....3..0
..2..0....3..1....2..0....2..1....3..0....2..1....3..1....3..1....3..0....3..0
CROSSREFS
Cf. A201981.
Sequence in context: A248528 A336493 A296247 * A109670 A014697 A328103
KEYWORD
nonn
AUTHOR
R. H. Hardin, Dec 07 2011
STATUS
approved