A239358 - OEIS

%I #8 Oct 25 2018 12:24:22

%S 6,16,32,60,106,156,218,299,399,524,680,874,1113,1404,1754,2170,2659,

%T 3228,3884,4634,5485,6444,7518,8714,10039,11500,13104,14858,16769,

%U 18844,21090,23514,26123,28924,31924,35130,38549,42188,46054,50154,54495,59084

%N Number of n X 5 0..2 arrays with no element equal to one plus the sum of elements to its left or one plus the sum of elements above it or one plus the sum of the elements diagonally to its northwest, modulo 3.

%H R. H. Hardin, <a href="/A239358/b239358.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = (7/6)*n^3 - (39/2)*n^2 + (538/3)*n - 486 for n>8.

%F Conjectures from _Colin Barker_, Oct 25 2018: (Start)

%F G.f.: x*(6 - 8*x + 4*x^2 + 4*x^3 - 20*x^5 + 22*x^6 - x^7 - 7*x^8 + 6*x^9 + x^11) / (1 - x)^4.

%F a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>4.

%F (End)

%e Some solutions for n=5:

%e ..0..0..0..0..2....0..0..0..0..0....0..0..0..0..2....0..0..0..0..0

%e ..0..0..0..0..2....0..0..0..0..0....0..0..0..0..2....0..0..0..0..2

%e ..0..0..2..2..0....0..0..0..2..2....0..0..0..0..0....0..0..0..0..2

%e ..0..0..2..2..1....0..0..0..2..1....0..2..2..0..0....0..0..0..0..0

%e ..2..2..0..1..1....0..0..0..0..2....2..2..1..2..0....2..2..0..0..0

%Y Column 5 of A239361.

%K nonn

%O 1,1

%A _R. H. Hardin_, Mar 17 2014