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%I A249983 #8 Nov 10 2018 05:46:34
%S A249983 20,88,208,426,728,1178,1744,2508,3420,4580,5920,7558,9408,11606,
%T A249983 14048,16888,20004,23568,27440,31810,36520,41778,47408,53636,60268,
%U A249983 67548,75264,83678,92560,102190,112320,123248,134708,147016,159888,173658,188024
%N A249983 Number of length 3+1 0..2*n arrays with the sum of the absolute values of adjacent differences equal to 3*n.
%H A249983 R. H. Hardin, <a href="/A249983/b249983.txt">Table of n, a(n) for n = 1..210</a>
%F A249983 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 A249983 Empirical for n mod 2 = 0: a(n) = (41/12)*n^3 + (43/4)*n^2 + (53/6)*n.
%F A249983 Empirical for n mod 2 = 1: a(n) = (41/12)*n^3 + (43/4)*n^2 + (79/12)*n - (3/4).
%F A249983 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 A249983 Some solutions for n=6:
%e A249983 ..9...11....5...12....2....4....5...11....4....7....0....0...11....8...12....4
%e A249983 ..1....1...11....4....0...11....0...10....2....0....8....1....1...12....4...12
%e A249983 ..2....4....2...10...10....6...10....2...10....1...10...10....0....0....3....7
%e A249983 .11....9....5....6....4....0....7...11....2...11....2....2....7....2...12...12
%Y A249983 Row 3 of A249982.
%K A249983 nonn
%O A249983 1,1
%A A249983 _R. H. Hardin_, Nov 10 2014

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