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A202080 Number of arrays of 9 integers in -n..n with sum zero and the sum of every adjacent pair being odd.

%I A202080 #7 Jul 22 2025 16:28:43
%S A202080 6,726,8412,80812,340660,1516410,4213042,12861252,28421280,69306670,
%T A202080 132493530,278307730,481381744,909136644,1461430338,2548699638,
%U A202080 3874036128,6350628468,9236088510,14409332790,20220953874,30295374604
%N A202080 Number of arrays of 9 integers in -n..n with sum zero and the sum of every adjacent pair being odd.
%C A202080 Row 7 of A202076
%H A202080 R. H. Hardin, <a href="/A202080/b202080.txt">Table of n, a(n) for n = 1..210</a>
%F A202080 Empirical: a(n) = a(n-1) +8*a(n-2) -8*a(n-3) -28*a(n-4) +28*a(n-5) +56*a(n-6) -56*a(n-7) -70*a(n-8) +70*a(n-9) +56*a(n-10) -56*a(n-11) -28*a(n-12) +28*a(n-13) +8*a(n-14) -8*a(n-15) -a(n-16) +a(n-17)
%e A202080 Some solutions for n=3
%e A202080 ..0...-2...-2....2....2....2....2....2....0....0...-2...-2....2....0....0....2
%e A202080 ..1....3....3....3....3....1...-1...-3...-1....1...-3....3....3....3...-1...-1
%e A202080 .-2....2....0....2...-2....2...-2....0....2...-2...-2...-2....2....0....2....0
%e A202080 ..1...-3....3...-1...-3....1....3...-1...-3....3....1....1...-1....3....1....1
%e A202080 ..0....0....2....0....2....0...-2....0...-2...-2....0...-2...-2...-2....2....0
%e A202080 ..1....3...-3...-3....3...-1....1....3....3...-3....3....3...-3...-3...-1...-3
%e A202080 .-2....0...-2...-2...-2...-2....0...-2...-2....2....2...-2....0....2....0...-2
%e A202080 ..1...-1...-1...-1...-3...-3....1....3....1....3....3....3...-1...-3...-1....1
%e A202080 ..0...-2....0....0....0....0...-2...-2....2...-2...-2...-2....0....0...-2....2
%K A202080 nonn
%O A202080 1,1
%A A202080 _R. H. Hardin_ Dec 10 2011