A194999 Number of lower triangles of a 3 X 3 0..n array with each element differing from all of its horizontal and vertical neighbors by one.

2, 20, 42, 66, 90, 114, 138, 162, 186, 210, 234, 258, 282, 306, 330, 354, 378, 402, 426, 450, 474, 498, 522, 546, 570, 594, 618, 642, 666, 690, 714, 738, 762, 786, 810, 834, 858, 882, 906, 930, 954, 978, 1002, 1026, 1050, 1074, 1098, 1122, 1146, 1170, 1194, 1218

Offset

1,1

Comments

Row 3 of A194998.

Links

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

Formula

Empirical: a(n) = 24*n - 30 for n>2.

Empirical g.f.: 2*x*(1 + 8*x + 2*x^2 + x^3) / (1 - x)^2. - Colin Barker, May 06 2018

Example

Some solutions for n=4:
..2......0......4......1......2......1......4......2......3......1......4
..3.2....1.2....3.2....2.1....1.2....2.3....3.4....1.2....4.3....2.3....3.2
..4.3.4..2.1.0..4.3.4..3.2.3..0.1.2..3.2.3..2.3.4..0.1.0..3.2.1..3.2.1..2.1.0

Crossrefs

Cf. A194998.

Sequence in context: A269669 A293930 A357485 * A280436 A266842 A254542

Adjacent sequences: A194996 A194997 A194998 * A195000 A195001 A195002

Keyword

nonn

Author

R. H. Hardin, Sep 07 2011

Status

approved