A193696 - OEIS

%I #5 Mar 31 2012 12:36:21

%S 1,5,23,83,299,1081,3931,14293,51955,188859,686519,2495537,9071325,

%T 32974351,119862177,435700975,1583780905,5757072535,20927062737,

%U 76070247573,276516705575,1005143149813,3653713262601,13281312856865

%N Number of arrays of -2..2 integers x(1..n) with every x(i) in a subsequence of length 1, 2 or 3 with sum zero

%C Column 2 of A193702

%H R. H. Hardin, <a href="/A193696/b193696.txt">Table of n, a(n) for n = 1..200</a>

%F Empirical: a(n) = 3*a(n-1) +2*a(n-2) -2*a(n-3) +5*a(n-4) +16*a(n-5) +18*a(n-6) +20*a(n-7) +23*a(n-8) +18*a(n-9) +7*a(n-10) +a(n-11) +4*a(n-12) +7*a(n-13) +a(n-14) -7*a(n-15) -8*a(n-16) -4*a(n-17) -a(n-18)

%e Some solutions for n=6

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

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

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

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

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

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

%K nonn

%O 1,2

%A _R. H. Hardin_ Aug 02 2011