A201348 Number of n X 3 0..1 arrays with rows and columns lexicographically nondecreasing and every element equal to at least one horizontal or vertical neighbor.

2, 8, 18, 47, 118, 273, 585, 1174, 2228, 4030, 6992, 11697, 18950, 29839, 45807, 68736, 101044, 145796, 206830, 288899, 397830, 540701, 726037, 964026, 1266756, 1648474, 2125868, 2718373, 3448502, 4342203, 5429243, 6743620, 8324004, 10214208

Offset

1,1

Comments

Column 3 of A201353.

Links

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

Formula

Empirical: a(n) = (1/5040)*n^7 - (1/720)*n^6 + (37/720)*n^5 - (53/144)*n^4 + (239/90)*n^3 - (2927/360)*n^2 + (1931/140)*n - 4 for n>1.

Conjectures from Colin Barker, May 22 2018: (Start)

G.f.: x*(2 - 8*x + 10*x^2 + 15*x^3 - 62*x^4 + 85*x^5 - 59*x^6 + 20*x^7 - 2*x^8) / (1 - x)^8.

a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8) for n>9.

(End)

Example

Some solutions for n=10:
..0..0..1....0..0..0....0..0..1....0..0..1....0..0..0....0..0..1....0..0..1
..0..0..1....0..1..1....0..1..1....0..0..1....0..1..1....0..0..1....0..0..1
..0..1..0....1..0..0....0..1..1....0..0..1....0..1..1....0..1..0....0..1..0
..0..1..0....1..0..0....1..1..0....0..0..1....0..1..1....0..1..0....0..1..0
..0..1..1....1..0..0....1..1..0....0..1..0....0..1..1....0..1..1....0..1..1
..0..1..1....1..0..0....1..1..1....0..1..0....0..1..1....1..0..1....0..1..1
..1..0..1....1..0..1....1..1..1....0..1..0....0..1..1....1..0..1....0..1..1
..1..0..1....1..0..1....1..1..1....0..1..1....0..1..1....1..0..1....0..1..1
..1..0..1....1..0..1....1..1..1....1..0..0....1..0..0....1..1..0....1..0..0
..1..1..1....1..1..1....1..1..1....1..1..0....1..0..0....1..1..0....1..0..0

Crossrefs

Cf. A201353.

Sequence in context: A073307 A064009 A246148 * A102713 A332217 A249763

Adjacent sequences: A201345 A201346 A201347 * A201349 A201350 A201351

Keyword

nonn

Author

R. H. Hardin, Nov 30 2011

Status

approved