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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.

%I A202069 #8 Jul 22 2025 16:27:49
%S A202069 2,4,2,0,6,12,6,0,20,40,20,0,70,140,70,0,252,504,252,0,924,1848,924,0,
%T A202069 3432,6864,3432,0,12870,25740,12870,0,48620,97240,48620,0,184756,
%U A202069 369512,184756,0,705432,1410864,705432,0,2704156,5408312,2704156,0,10400600
%N A202069 Number of arrays of n+2 integers in -1..1 with sum zero and the sum of every adjacent pair being odd.
%C A202069 Column 1 of A202076
%H A202069 R. H. Hardin, <a href="/A202069/b202069.txt">Table of n, a(n) for n = 1..210</a>
%F A202069 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)
%e A202069 Some solutions for n=10
%e A202069 ..0....1...-1....1....0...-1....0....1....1....0....0....0....0...-1....0...-1
%e A202069 ..1....0....0....0....1....0...-1....0....0....1...-1....1...-1....0...-1....0
%e A202069 ..0...-1...-1...-1....0....1....0....1....1....0....0....0....0....1....0...-1
%e A202069 ..1....0....0....0...-1....0....1....0....0...-1...-1....1....1....0....1....0
%e A202069 ..0...-1....1...-1....0....1....0...-1....1....0....0....0....0....1....0...-1
%e A202069 ..1....0....0....0....1....0....1....0....0....1....1...-1...-1....0....1....0
%e A202069 ..0...-1....1....1....0...-1....0....1...-1....0....0....0....0...-1....0....1
%e A202069 .-1....0....0....0....1....0...-1....0....0...-1....1...-1....1....0...-1....0
%e A202069 ..0....1....1....1....0....1....0...-1...-1....0....0....0....0...-1....0....1
%e A202069 .-1....0....0....0...-1....0....1....0....0...-1....1....1...-1....0...-1....0
%e A202069 ..0....1...-1...-1....0...-1....0...-1...-1....0....0....0....0....1....0....1
%e A202069 .-1....0....0....0...-1....0...-1....0....0....1...-1...-1....1....0....1....0
%K A202069 nonn
%O A202069 1,1
%A A202069 _R. H. Hardin_ Dec 10 2011