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%I #8 Nov 10 2018 05:46:27
%S 64,384,1242,3030,6252,11524,19574,31242,47480,69352,98034,134814,
%T 181092,238380,308302,392594,493104,611792,750730,912102,1098204,
%U 1311444,1554342,1829530,2139752,2487864,2876834,3309742,3789780,4320252,4904574
%N Number of length 4+1 0..2*n arrays with the sum of the absolute values of adjacent differences equal to 4*n.
%H R. H. Hardin, <a href="/A249984/b249984.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = (14/3)*n^4 + (56/3)*n^3 + (121/3)*n^2 - (5/3)*n + 2.
%F Conjectures from _Colin Barker_, Nov 10 2018: (Start)
%F G.f.: 2*x*(32 + 32*x - 19*x^2 + 10*x^3 + x^4) / (1 - x)^5.
%F a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>5.
%F (End)
%e Some solutions for n=6:
%e ..3...12....2....1....6....9...12....2....8...12....3....2...11...12....2....2
%e ..0....0....9...11....2....3....2...11....0....6...11....6...12....1...12....9
%e .12....6....1....8...10....8...10....9....9...11....0...12....0....7....3....1
%e .10....6....1....0....5....2....6...11....3....0....1....5....4....2....7....3
%e ..3....0...10....3...12....9....8....0....4....2....5...12...11....0....6...10
%Y Row 4 of A249982.
%K nonn
%O 1,1
%A _R. H. Hardin_, Nov 10 2014
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