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A202077 Number of arrays of 5 integers in -n..n with sum zero and the sum of every adjacent pair being odd.

%I A202077 #12 May 26 2018 08:45:20
%S A202077 2,26,78,264,504,1128,1786,3262,4660,7540,10092,15066,19278,27174,
%T A202077 33644,45428,54846,71622,84770,107780,125532,156156,179478,219234,
%U A202077 249184,299728,337456,400582,447330,524970,582072,676296,745178,858194,940374
%N A202077 Number of arrays of 5 integers in -n..n with sum zero and the sum of every adjacent pair being odd.
%C A202077 Row 3 of A202076.
%H A202077 R. H. Hardin, <a href="/A202077/b202077.txt">Table of n, a(n) for n = 1..210</a>
%F A202077 Empirical: a(n) = a(n-1) + 4*a(n-2) - 4*a(n-3) - 6*a(n-4) + 6*a(n-5) + 4*a(n-6) - 4*a(n-7) - a(n-8) + a(n-9).
%F A202077 Conjectures from _Colin Barker_, May 26 2018: (Start)
%F A202077 G.f.: 2*x*(1 + 12*x + 22*x^2 + 45*x^3 + 22*x^4 + 12*x^5 + x^6) / ((1 - x)^5*(1 + x)^4).
%F A202077 a(n) = (230*n^4 + 552*n^3 + 424*n^2 + 96*n) / 384 for n even.
%F A202077 a(n) = (230*n^4 + 368*n^3 + 148*n^2 + 16*n + 6) / 384 for n odd.
%F A202077 (End)
%e A202077 Some solutions for n=3:
%e A202077   -2  0  0 -2  0  2  0  0  2  2 -2  2  2  2 -2  2
%e A202077   -1 -1 -3  1 -1 -1 -1  3  1 -3  3  1 -3 -3  1 -3
%e A202077    0  2  2  0  0  0  2 -2 -2 -2  2  0  0  2 -2  0
%e A202077    1 -3  1 -1 -1 -1  1 -1 -1  3 -3 -3 -1 -1  3  3
%e A202077    2  2  0  2  2  0 -2  0  0  0  0  0  2  0  0 -2
%Y A202077 Cf. A202076.
%K A202077 nonn
%O A202077 1,1
%A A202077 _R. H. Hardin_, Dec 10 2011