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%I #12 Sep 10 2018 10:11:53
%S 25,319,2511,13933,58911,242461,989527,4017157,16245775,65514541,
%T 263652487,1059392917,4251920575,17050729021,68332056247,273715645477,
%U 1096024843375,4387586157901,17560804984807,70274600998837
%N Number of third differences of arrays of length n+3 of numbers in 0..3.
%H R. H. Hardin, <a href="/A228255/b228255.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 7*a(n-1) - 12*a(n-2) for n>7.
%F Conjectures from _Colin Barker_, Sep 10 2018: (Start)
%F G.f.: x*(25 + 144*x + 578*x^2 + 184*x^3 - 8488*x^4 - 2720*x^5 - 768*x^6) / ((1 - 3*x)*(1 - 4*x)).
%F a(n) = 4^(3+n) - 3^(3+n) for n>5.
%F (End)
%e Some solutions for n=4:
%e .-7....4....0...-5...-5..-12....5....1..-11...-1....7...-5....6....3....8...-3
%e .10...-1....0....7....1...10..-10....1....9....1...-1....4...-9...-1...-8....5
%e .-9...-3...-6....0...-1...-6....9....2....0...-3...-4....3....7....2....3..-10
%e ..6....1....9...-8....5....4...-3...-2...-7....4....6...-9...-2...-7....4...12
%Y Column 3 of A228260.
%K nonn
%O 1,1
%A _R. H. Hardin_, Aug 19 2013