A195233 Number of lower triangles of a 3 X 3 0..n array with each element differing from all of its diagonal, vertical, antidiagonal and horizontal neighbors by one or less.

64, 155, 246, 337, 428, 519, 610, 701, 792, 883, 974, 1065, 1156, 1247, 1338, 1429, 1520, 1611, 1702, 1793, 1884, 1975, 2066, 2157, 2248, 2339, 2430, 2521, 2612, 2703, 2794, 2885, 2976, 3067, 3158, 3249, 3340, 3431, 3522, 3613, 3704, 3795, 3886, 3977

Offset

1,1

Comments

Row 3 of A195232.

Links

R. H. Hardin, Table of n, a(n) for n = 1..200

Formula

Empirical: a(n) = 91*n - 27.

Conjectures from Colin Barker, May 06 2018: (Start)

G.f.: x*(64 + 27*x) / (1 - x)^2.

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

(End)

Example

Some solutions for n=4:
..2......1......0......2......1......3......2......0......4......3......0
..2.3....2.1....0.1....1.1....0.0....2.2....2.1....0.1....3.3....4.3....0.0
..2.3.3..1.1.2..0.1.1..2.2.1..0.0.0..2.2.1..2.1.1..1.0.0..3.4.4..3.3.4..0.1.1

Crossrefs

Cf. A195232.

Sequence in context: A044315 A044696 A235120 * A086052 A044396 A044777

Adjacent sequences: A195230 A195231 A195232 * A195234 A195235 A195236

Keyword

nonn

Author

R. H. Hardin, Sep 13 2011

Status

approved