A201975 - OEIS

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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.

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

Column 2 of A201981.

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..210

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

Adjacent sequences: A201972 A201973 A201974 * A201976 A201977 A201978

KEYWORD

nonn

AUTHOR

R. H. Hardin, Dec 07 2011

STATUS

approved