A201722 Number of n X 1 0..4 arrays with rows and columns lexicographically nondecreasing and no element equal to the number of horizontal and vertical neighbors equal to itself.

4, 10, 20, 35, 56, 83, 116, 155, 200, 251, 308, 371, 440, 515, 596, 683, 776, 875, 980, 1091, 1208, 1331, 1460, 1595, 1736, 1883, 2036, 2195, 2360, 2531, 2708, 2891, 3080, 3275, 3476, 3683, 3896, 4115, 4340, 4571, 4808, 5051, 5300, 5555, 5816, 6083, 6356

Offset

1,1

Comments

Column 1 of A201729.

Links

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

Formula

Empirical: a(n) = 3*n^2 - 6*n + 11 for n>2.

Conjectures from Colin Barker, May 23 2018: (Start)

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

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>5.

(End)

Example

Some solutions for n=8.
..0....3....1....0....0....0....0....1....0....0....0....0....0....0....0....0
..0....3....3....0....0....0....0....3....0....0....0....0....0....0....0....0
..0....3....3....0....0....0....0....3....0....2....0....2....0....0....0....0
..1....3....3....0....0....4....1....3....0....3....0....3....1....1....0....3
..2....4....3....0....2....4....2....4....0....3....2....4....4....2....4....4
..4....4....3....2....3....4....3....4....3....3....3....4....4....2....4....4
..4....4....4....2....3....4....3....4....4....3....3....4....4....3....4....4
..4....4....4....3....3....4....4....4....4....3....4....4....4....3....4....4

Crossrefs

Cf. A201729.

Sequence in context: A038409 A374710 A347252 * A352208 A341193 A090579

Adjacent sequences: A201719 A201720 A201721 * A201723 A201724 A201725

Keyword

nonn

Author

R. H. Hardin, Dec 04 2011

Status

approved