A221962 - OEIS

%I #9 Aug 11 2018 13:08:39

%S 7,49,175,833,3647,16513,73983,332801,1495039,6719489,30195711,

%T 135700481,609828863,2740551681,12315918335,55347249153,248728256511,

%U 1117774675969,5023233736703,22574207598593,101447567933439,455901232234497

%N Number of -3..3 arrays of length n with the sum ahead of each element differing from the sum following that element by 3 or less.

%C Column 3 of A221967.

%H R. H. Hardin, <a href="/A221962/b221962.txt">Table of n, a(n) for n = 1..144</a>

%F Empirical: a(n) = 3*a(n-1) + 8*a(n-2) - 4*a(n-3) - 8*a(n-4).

%F Empirical g.f.: 7*x*(1 + 4*x - 4*x^2 - 8*x^3) / ((1 + x)*(1 - 4*x - 4*x^2 + 8*x^3)). - _Colin Barker_, Aug 11 2018

%e Some solutions for n=6:

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

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

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

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

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

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

%Y Cf. A221967.

%K nonn

%O 1,1

%A _R. H. Hardin_, Feb 01 2013