A195236 Number of lower triangles of a 6 X 6 0..n array with each element differing from all of its diagonal, vertical, antidiagonal and horizontal neighbors by one or less.

2097152, 10322065, 20729610, 31374671, 42029278, 52683885, 63338492, 73993099, 84647706, 95302313, 105956920, 116611527, 127266134, 137920741, 148575348, 159229955, 169884562, 180539169, 191193776, 201848383, 212502990, 223157597

Offset

1,1

Comments

Row 6 of A195232.

Links

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

Formula

Empirical: a(n) = 10654607*n - 11243757 for n>3.

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

G.f.: x*(2097152 + 6127761*x + 2182632*x^2 + 237516*x^3 + 9546*x^4) / (1 - x)^2.

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

(End)

Example

Some solutions for n=5 with 0 and 5:
..5............5............5............0............5............0
..4.4..........4.4..........4.4..........0.1..........4.4..........1.1
..4.3.3........4.3.3........3.3.3........1.1.2........3.3.3........2.1.2
..3.3.3.2......4.3.3.2......3.2.2.2......1.2.2.3......2.2.2.2......1.1.2.3
..3.2.2.2.1....4.4.3.2.1....2.2.2.1.1....2.2.3.3.4....1.1.1.2.2....2.1.2.3.4
..2.2.1.2.1.0..4.3.3.2.1.0..3.2.2.1.0.0..2.3.2.3.4.5..0.1.1.2.1.2..1.2.2.3.4.5

Crossrefs

Cf. A195232.

Sequence in context: A126435 A011571 A022537 * A386526 A068345 A194935

Adjacent sequences: A195233 A195234 A195235 * A195237 A195238 A195239

Keyword

nonn

Author

R. H. Hardin, Sep 13 2011

Status

approved