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%I #8 Sep 07 2018 03:04:19
%S 10,40,124,329,777,1673,3341,6269,11164,19018,31186,49477,76259,
%T 114579,168299,242249,342398,476044,652024,880945,1175437,1550429,
%U 2023449,2614949,3348656,4251950,5356270,6697549,8316679,10260007,12579863
%N Number of n X 2 -2..2 arrays of 2 X 2 subblock diagonal sums minus antidiagonal sums for some (n+1) X 3 binary array with rows and columns of the latter in lexicographically nondecreasing order.
%H R. H. Hardin, <a href="/A227056/b227056.txt">Table of n, a(n) for n = 1..54</a>
%F Empirical: a(n) = (1/5040)*n^7 + (1/180)*n^6 + (23/360)*n^5 + (25/72)*n^4 + (907/720)*n^3 + (1133/360)*n^2 + (877/210)*n + 1.
%F Conjectures from _Colin Barker_, Sep 07 2018: (Start)
%F G.f.: x*(10 - 40*x + 84*x^2 - 103*x^3 + 77*x^4 - 35*x^5 + 9*x^6 - x^7) / (1 - x)^8.
%F a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8) for n>8.
%F (End)
%e Some solutions for n=3:
%e ..0..0....1.-2....0..0...-2..1....0..0....1.-1....1.-1....0..0....0..1....0..1
%e ..1..0...-1..1....0..0....0..0....1..0....0..0....0..0....0.-1....1.-2....1.-1
%e .-2..1....0..0....0..0....1.-1...-1..0...-2..1...-1..0....0..0...-1..1...-2..0
%Y Column 2 of A227060.
%K nonn
%O 1,1
%A _R. H. Hardin_, Jun 30 2013
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