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A202078 Number of arrays of 7 integers in -n..n with sum zero and the sum of every adjacent pair being odd.

%I A202078 #7 Jul 22 2025 16:28:36
%S A202078 6,96,1014,3752,15010,35604,95342,181834,390544,654086,1221708,
%T A202078 1876930,3183404,4598874,7268148,10026924,15014418,19984692,28678218,
%U A202078 37094052,51428190,64980344,87564274,108501126,142759916,173998474,224327824
%N A202078 Number of arrays of 7 integers in -n..n with sum zero and the sum of every adjacent pair being odd.
%C A202078 Row 5 of A202076
%H A202078 R. H. Hardin, <a href="/A202078/b202078.txt">Table of n, a(n) for n = 1..210</a>
%F A202078 Empirical: a(n) = a(n-1) +6*a(n-2) -6*a(n-3) -15*a(n-4) +15*a(n-5) +20*a(n-6) -20*a(n-7) -15*a(n-8) +15*a(n-9) +6*a(n-10) -6*a(n-11) -a(n-12) +a(n-13)
%e A202078 Some solutions for n=3
%e A202078 ..1...-1....3....1...-3...-3....3....3....1...-3....1....1....3...-1...-1...-1
%e A202078 ..2....0...-2....0....0....0...-2...-2....0...-2....2...-2....0...-2....0....2
%e A202078 ..1....1....1...-1....1...-1...-3....1...-3....1....1....3....1....1....3...-1
%e A202078 ..2....2....2....0....0...-2...-2...-2....2...-2...-2....2...-2...-2....0....0
%e A202078 .-3....1....1....1....1....3....3....3...-1....3...-3...-3...-3....3...-1...-1
%e A202078 .-2....0...-2...-2....0....0...-2...-2....0....2....0...-2....0....0...-2....0
%e A202078 .-1...-3...-3....1....1....3....3...-1....1....1....1....1....1....1....1....1
%K A202078 nonn
%O A202078 1,1
%A A202078 _R. H. Hardin_ Dec 10 2011