A220033 Number of 3 X n 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..1 3 X n array.

4, 6, 10, 19, 30, 42, 55, 69, 84, 100, 117, 135, 154, 174, 195, 217, 240, 264, 289, 315, 342, 370, 399, 429, 460, 492, 525, 559, 594, 630, 667, 705, 744, 784, 825, 867, 910, 954, 999, 1045, 1092, 1140, 1189, 1239, 1290, 1342, 1395, 1449, 1504, 1560, 1617, 1675

Offset

1,1

Comments

Row 3 of A220032.

Links

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

Formula

Empirical: a(n) = (1/2)*n^2 + (13/2)*n - 15 for n>3.

Conjectures from Colin Barker, Jul 30 2018: (Start)

G.f.: x*(4 - 6*x + 4*x^2 + 3*x^3 - 3*x^4 - x^5) / (1 - x)^3.

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>6.

(End)

Example

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

Crossrefs

Cf. A220032.

Sequence in context: A108900 A076995 A096817 * A277455 A320124 A185913

Adjacent sequences: A220030 A220031 A220032 * A220034 A220035 A220036

Keyword

nonn

Author

R. H. Hardin, Dec 03 2012

Status

approved