A193695 - OEIS

%I #8 Feb 19 2015 14:43:48

%S 1,3,9,23,57,141,351,875,2181,5435,13543,33747,84093,209549,522169,

%T 1301177,3242363,8079545,20133171,50169233,125015177,311521495,

%U 776270883,1934365665,4820186623,12011275583,29930530167,74582972465,185851027385

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

%C Column 1 of A193702

%H R. H. Hardin, <a href="/A193695/b193695.txt">Table of n, a(n) for n = 1..200</a>

%F Empirical: a(n) = 2*a(n-1) +a(n-2) +a(n-4) +a(n-5).

%F Empirical: G.f.: x*( -1-x-2*x^2-2*x^3-x^4 ) / ( -1+2*x+x^2+x^4+x^5 ). - _R. J. Mathar_, Feb 19 2015

%e Some solutions for n=6

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

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

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

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

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

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

%K nonn

%O 1,2

%A _R. H. Hardin_ Aug 02 2011