A219589 Number of n X 2 arrays of the minimum value of corresponding elements and their horizontal or vertical neighbors in a random, but sorted with lexicographically nondecreasing rows and nonincreasing columns, 0..2 n X 2 array.

3, 7, 21, 46, 87, 151, 247, 386, 581, 847, 1201, 1662, 2251, 2991, 3907, 5026, 6377, 7991, 9901, 12142, 14751, 17767, 21231, 25186, 29677, 34751, 40457, 46846, 53971, 61887, 70651, 80322, 90961, 102631, 115397, 129326, 144487, 160951, 178791

Offset

1,1

Comments

Column 2 of A219595.

Links

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

Formula

Empirical: a(n) = (1/12)*n^4 - (1/3)*n^3 + (47/12)*n^2 - (14/3)*n + 2 for n>1.

Conjectures from Colin Barker, Mar 12 2018: (Start)

G.f.: x*(3 - 8*x + 16*x^2 - 19*x^3 + 12*x^4 - 2*x^5) / (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>6.

(End)

Example

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

Crossrefs

Cf. A219595.

Sequence in context: A018712 A183936 A027151 * A092203 A018760 A050614

Adjacent sequences: A219586 A219587 A219588 * A219590 A219591 A219592

Keyword

nonn

Author

R. H. Hardin, Nov 23 2012

Status

approved