A193642 - OEIS

%I #9 Feb 19 2015 14:13:00

%S 1,5,13,37,105,297,841,2381,6741,19085,54033,152977,433105,1226197,

%T 3471581,9828661,27826681,78782265,223046553,631484317,1787844005,

%U 5061703197,14330578721,40572407841,114867676321,325210747045

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

%C Column 2 of A193648

%H R. H. Hardin, <a href="/A193642/b193642.txt">Table of n, a(n) for n = 1..200</a>

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

%F Empirical: G.f.: -x*(1+3*x+x^2) / ( -1+2*x+2*x^2+x^3 ). - _R. J. Mathar_, Feb 19 2015

%e Some solutions for n=6

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

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

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

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

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

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

%K nonn

%O 1,2

%A _R. H. Hardin_ Aug 02 2011