cp's OEIS Frontend

A193695 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.

%I A193695 #10 Jul 22 2025 12:27:55
%S A193695 1,3,9,23,57,141,351,875,2181,5435,13543,33747,84093,209549,522169,
%T A193695 1301177,3242363,8079545,20133171,50169233,125015177,311521495,
%U A193695 776270883,1934365665,4820186623,12011275583,29930530167,74582972465,185851027385
%N A193695 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 A193695 Column 1 of A193702
%H A193695 R. H. Hardin, <a href="/A193695/b193695.txt">Table of n, a(n) for n = 1..200</a>
%F A193695 Empirical: a(n) = 2*a(n-1) +a(n-2) +a(n-4) +a(n-5).
%F A193695 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 A193695 Some solutions for n=6
%e A193695 .-1....0....1....0....0....0....0....0....1...-1....1....1....0....1...-1....0
%e A193695 ..1...-1...-1....0....0....0...-1....1...-1....1...-1...-1....0...-1....1...-1
%e A193695 ..0....1....1....0....1....0....0...-1....0....1....1....1....1....1...-1....1
%e A193695 ..0....0....1....1....0...-1....1....0....0...-1...-1....0...-1...-1....0...-1
%e A193695 ..1...-1...-1...-1...-1....1....1....0....1....0....1....0....0....0....1....1
%e A193695 .-1....0....0....1....1....0...-1....0...-1....0...-1....0....0....1...-1....0
%K A193695 nonn
%O A193695 1,2
%A A193695 _R. H. Hardin_ Aug 02 2011