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.

1, 3, 9, 23, 57, 141, 351, 875, 2181, 5435, 13543, 33747, 84093, 209549, 522169, 1301177, 3242363, 8079545, 20133171, 50169233, 125015177, 311521495, 776270883, 1934365665, 4820186623, 12011275583, 29930530167, 74582972465, 185851027385

Offset: 1

Author

R. H. Hardin Aug 02 2011

Keywords

• nonn

Comments

Column 1 of A193702

Examples

			Some solutions for n=6
.-1....0....1....0....0....0....0....0....1...-1....1....1....0....1...-1....0
..1...-1...-1....0....0....0...-1....1...-1....1...-1...-1....0...-1....1...-1
..0....1....1....0....1....0....0...-1....0....1....1....1....1....1...-1....1
..0....0....1....1....0...-1....1....0....0...-1...-1....0...-1...-1....0...-1
..1...-1...-1...-1...-1....1....1....0....1....0....1....0....0....0....1....1
.-1....0....0....1....1....0...-1....0...-1....0...-1....0....0....1...-1....0
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..200

Formula

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

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