A228213 - OEIS

%I #9 Sep 29 2023 07:58:13

%S 13,103,625,3151,14053,58975,242461,989527,4017157,16245775,65514541,

%T 263652487,1059392917,4251920575,17050729021,68332056247,273715645477,

%U 1096024843375,4387586157901,17560804984807,70274600998837

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

%H R. H. Hardin, <a href="/A228213/b228213.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 7*a(n-1) - 12*a(n-2) = A005061(n+2) for n>7.

%F Conjectures from _Colin Barker_, Sep 09 2018: (Start)

%F G.f.: x*(13 + 12*x + 60*x^2 + 12*x^3 - 504*x^4 - 1584*x^5 - 1728*x^6) / ((1 - 3*x)*(1 - 4*x)).

%F a(n) = 4^(2+n) - 3^(2+n) for n>5.

%F (End)

%e Some solutions for n=4:

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

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

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

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

%Y Column 3 of A228218.

%K nonn

%O 1,1

%A _R. H. Hardin_, Aug 16 2013