A202069 Number of arrays of n+2 integers in -1..1 with sum zero and the sum of every adjacent pair being odd.

2, 4, 2, 0, 6, 12, 6, 0, 20, 40, 20, 0, 70, 140, 70, 0, 252, 504, 252, 0, 924, 1848, 924, 0, 3432, 6864, 3432, 0, 12870, 25740, 12870, 0, 48620, 97240, 48620, 0, 184756, 369512, 184756, 0, 705432, 1410864, 705432, 0, 2704156, 5408312, 2704156, 0, 10400600

Offset: 1

Author

R. H. Hardin Dec 10 2011

Keywords

• nonn

Comments

Column 1 of A202076

Examples

			Some solutions for n=10
..0....1...-1....1....0...-1....0....1....1....0....0....0....0...-1....0...-1
..1....0....0....0....1....0...-1....0....0....1...-1....1...-1....0...-1....0
..0...-1...-1...-1....0....1....0....1....1....0....0....0....0....1....0...-1
..1....0....0....0...-1....0....1....0....0...-1...-1....1....1....0....1....0
..0...-1....1...-1....0....1....0...-1....1....0....0....0....0....1....0...-1
..1....0....0....0....1....0....1....0....0....1....1...-1...-1....0....1....0
..0...-1....1....1....0...-1....0....1...-1....0....0....0....0...-1....0....1
.-1....0....0....0....1....0...-1....0....0...-1....1...-1....1....0...-1....0
..0....1....1....1....0....1....0...-1...-1....0....0....0....0...-1....0....1
.-1....0....0....0...-1....0....1....0....0...-1....1....1...-1....0...-1....0
..0....1...-1...-1....0...-1....0...-1...-1....0....0....0....0....1....0....1
.-1....0....0....0...-1....0...-1....0....0....1...-1...-1....1....0....1....0
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..210

Formula

Empirical: a(n) = f(n mod 4) * binomial(2*z,z), where f(1)=1, f(2)=2, f(3)=1, f(0)=0, and z=floor((n+3)/4)