%I #8 Nov 10 2018 05:46:34

%S 20,88,208,426,728,1178,1744,2508,3420,4580,5920,7558,9408,11606,

%T 14048,16888,20004,23568,27440,31810,36520,41778,47408,53636,60268,

%U 67548,75264,83678,92560,102190,112320,123248,134708,147016,159888,173658,188024

%N Number of length 3+1 0..2*n arrays with the sum of the absolute values of adjacent differences equal to 3*n.

%H R. H. Hardin, <a href="/A249983/b249983.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 2*a(n-1) + a(n-2) - 4*a(n-3) + a(n-4) + 2*a(n-5) - a(n-6).

%F Empirical for n mod 2 = 0: a(n) = (41/12)*n^3 + (43/4)*n^2 + (53/6)*n.

%F Empirical for n mod 2 = 1: a(n) = (41/12)*n^3 + (43/4)*n^2 + (79/12)*n - (3/4).

%F Empirical g.f.: 2*x*(10 + 24*x + 6*x^2 + x^3) / ((1 - x)^4*(1 + x)^2). - _Colin Barker_, Nov 10 2018

%e Some solutions for n=6:

%e ..9...11....5...12....2....4....5...11....4....7....0....0...11....8...12....4

%e ..1....1...11....4....0...11....0...10....2....0....8....1....1...12....4...12

%e ..2....4....2...10...10....6...10....2...10....1...10...10....0....0....3....7

%e .11....9....5....6....4....0....7...11....2...11....2....2....7....2...12...12

%Y Row 3 of A249982.

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 10 2014