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A193696 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.

%I A193696 #7 Jul 22 2025 12:28:02
%S A193696 1,5,23,83,299,1081,3931,14293,51955,188859,686519,2495537,9071325,
%T A193696 32974351,119862177,435700975,1583780905,5757072535,20927062737,
%U A193696 76070247573,276516705575,1005143149813,3653713262601,13281312856865
%N A193696 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 A193696 Column 2 of A193702
%H A193696 R. H. Hardin, <a href="/A193696/b193696.txt">Table of n, a(n) for n = 1..200</a>
%F A193696 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 A193696 Some solutions for n=6
%e A193696 .-1....0....1...-2...-1...-2....2...-1...-1....0....1....0...-1...-1...-2....1
%e A193696 ..0...-1....0....0....1....2....0...-1....2....1...-1....1....1...-1....0...-1
%e A193696 ..1....1...-1....2...-1...-2...-2....2...-1...-1....0....1....1....2....2....2
%e A193696 ..1...-1....0...-1....1....1....1....0...-1...-2....2...-2...-2....1...-1...-2
%e A193696 .-1...-2....1...-1...-2...-1....1....1...-2....1...-1...-1....1....0....1...-1
%e A193696 ..1....2....0....2....2....1...-2...-1....2....1...-1....1....0...-1...-1....1
%K A193696 nonn
%O A193696 1,2
%A A193696 _R. H. Hardin_ Aug 02 2011