A195237 Number of lower triangles of a 7 X 7 0..n array with each element differing from all of its diagonal, vertical, antidiagonal and horizontal neighbors by one or less.

268435456, 1663418313, 3601738548, 5618308863, 7640055854, 9661943973, 11683832092, 13705720211, 15727608330, 17749496449, 19771384568, 21793272687, 23815160806, 25837048925, 27858937044, 29880825163, 31902713282, 33924601401

Offset

1,1

Comments

Row 7 of A195232.

Links

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

Formula

Empirical: a(n) = 2021888119*n - 2469384741 for n>4.

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

G.f.: x*(268435456 + 1126547401*x + 543337378*x^2 + 78250080*x^3 + 5176676*x^4 + 141128*x^5) / (1 - x)^2.

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

(End)

Example

Some solutions for n=6 with 0 and 6:
..6..............0..............0..............0..............6
..5.5............1.1............1.1............1.1............5.5
..4.4.4..........2.2.2..........1.2.2..........2.2.2..........4.4.4
..4.3.3.3........3.3.3.3........1.1.2.3........2.3.3.3........3.3.3.3
..4.3.2.2.2......3.4.3.4.4......0.1.2.3.4......3.2.3.3.4......2.2.2.2.2
..3.3.3.2.2.1....3.4.4.4.5.5....1.1.2.3.4.5....2.3.2.3.4.5....1.2.2.2.1.1
..4.3.3.2.1.1.0..4.4.4.5.4.5.6..2.1.2.3.4.5.6..3.2.2.3.4.5.6..2.2.2.2.2.1.0

Crossrefs

Cf. A195232.

Sequence in context: A011578 A223605 A223698 * A194936 A195253 A122969

Adjacent sequences: A195234 A195235 A195236 * A195238 A195239 A195240

Keyword

nonn

Author

R. H. Hardin, Sep 13 2011

Status

approved