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

1,1

Comments

Column 1 of A202076

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)

Example

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

Crossrefs

Sequence in context: A356165 A366589 A335764 * A364529 A300329 A094239

Adjacent sequences: A202066 A202067 A202068 * A202070 A202071 A202072

Keyword

nonn

Author

R. H. Hardin Dec 10 2011

Status

approved