A228254 - OEIS

%I #13 Sep 10 2018 08:51:42

%S 17,143,621,2059,6305,19171,58025,175099,527345,1586131,4766585,

%T 14316139,42981185,129009091,387158345,1161737179,3485735825,

%U 10458256051,31376865305,94134790219,282412759265,847255055011,2541798719465

%N Number of third differences of arrays of length n+3 of numbers in 0..2.

%H R. H. Hardin, <a href="/A228254/b228254.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 5*a(n-1) - 6*a(n-2) for n>5.

%F Conjectures from _Colin Barker_, Sep 10 2018: (Start)

%F G.f.: x*(17 + 58*x + 8*x^2 - 188*x^3 - 264*x^4) / ((1 - 2*x)*(1 - 3*x)).

%F a(n) = 3^(3+n) - 2^(3+n) for n>3.

%F (End)

%e Some solutions for n=4:

%e .-7...-4....3....4....3....1....1...-7....3....1....4...-3...-4...-2...-7...-1

%e ..7....2....0...-6...-3....3....2....6....3....2...-2....4....0....3....7....2

%e .-4....2...-3....5....0...-5...-1...-1...-6...-4...-2...-3....3...-2...-3....0

%e ..2...-4....3...-3....3....7...-1...-1....4....4....3....0...-4...-2...-2...-1

%Y Column 2 of A228260.

%K nonn

%O 1,1

%A _R. H. Hardin_, Aug 19 2013