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A202069
Number of arrays of n+2 integers in -1..1 with sum zero and the sum of every adjacent pair being odd
2
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
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: A366589 A335764 A375054 * A364529 A300329 A094239
KEYWORD
nonn
AUTHOR
R. H. Hardin Dec 10 2011
STATUS
approved