A195237 - OEIS

%I #9 May 06 2018 12:18:37

%S 268435456,1663418313,3601738548,5618308863,7640055854,9661943973,

%T 11683832092,13705720211,15727608330,17749496449,19771384568,

%U 21793272687,23815160806,25837048925,27858937044,29880825163,31902713282,33924601401

%N 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.

%C Row 7 of A195232.

%H R. H. Hardin, <a href="/A195237/b195237.txt">Table of n, a(n) for n = 1..200</a>

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

%F Conjectures from _Colin Barker_, May 06 2018: (Start)

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

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

%F (End)

%e Some solutions for n=6 with 0 and 6:

%e ..6..............0..............0..............0..............6

%e ..5.5............1.1............1.1............1.1............5.5

%e ..4.4.4..........2.2.2..........1.2.2..........2.2.2..........4.4.4

%e ..4.3.3.3........3.3.3.3........1.1.2.3........2.3.3.3........3.3.3.3

%e ..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

%e ..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

%e ..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

%Y Cf. A195232.

%K nonn

%O 1,1

%A _R. H. Hardin_, Sep 13 2011