A195000 Number of lower triangles of a 4 X 4 0..n array with each element differing from all of its horizontal and vertical neighbors by one.

2, 80, 248, 458, 672, 888, 1104, 1320, 1536, 1752, 1968, 2184, 2400, 2616, 2832, 3048, 3264, 3480, 3696, 3912, 4128, 4344, 4560, 4776, 4992, 5208, 5424, 5640, 5856, 6072, 6288, 6504, 6720, 6936, 7152, 7368, 7584, 7800, 8016, 8232, 8448, 8664, 8880, 9096

Offset

1,1

Comments

Row 4 of A194998.

Links

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

Formula

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

G.f.: 2*x*(1 + 38*x + 45*x^2 + 21*x^3 + 2*x^4 + x^5) / (1 - x)^2.

a(n) = 24*(9*n - 17) for n>4.

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

(End)

Example

Some solutions for n=4:
..1........4........3........4........2........1........1........0
..2.1......3.2......2.3......3.2......3.4......0.1......2.1......1.2
..1.0.1....2.1.2....3.4.3....2.1.2....2.3.4....1.2.1....3.2.3....2.3.2
..0.1.0.1..1.2.3.4..2.3.2.1..1.0.1.0..3.4.3.2..2.1.2.1..2.3.2.3..3.2.1.0

Crossrefs

Cf. A194998.

Sequence in context: A100421 A319438 A371151 * A073499 A222826 A123828

Adjacent sequences: A194997 A194998 A194999 * A195001 A195002 A195003

Keyword

nonn

Author

R. H. Hardin, Sep 07 2011

Status

approved