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%I #7 Nov 10 2018 09:08:34
%S 136,1606,6856,22560,55372,123154,237348,434042,728724,1184066,
%T 1817540,2728080,3931760,5574774,7667096,10414498,13814832,18147086,
%U 23389648,29909680,37657444,47104554,58163164,71426938,86758620,104892842
%N Number of length 5+1 0..2*n arrays with the sum of the absolute values of adjacent differences equal to 5*n.
%H R. H. Hardin, <a href="/A249985/b249985.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 2*a(n-1) + 3*a(n-2) - 8*a(n-3) - 2*a(n-4) + 12*a(n-5) - 2*a(n-6) - 8*a(n-7) + 3*a(n-8) + 2*a(n-9) - a(n-10).
%F Empirical for n mod 2 = 0: a(n) = (1739/240)*n^5 + (3679/96)*n^4 + (859/12)*n^3 + (1121/24)*n^2 - (4/15)*n + 2.
%F Empirical for n mod 2 = 1: a(n) = (1739/240)*n^5 + (3679/96)*n^4 + (1553/24)*n^3 + (1357/48)*n^2 - (949/240)*n + (45/32).
%F Empirical g.f.: 2*x*(68 + 667*x + 1618*x^2 + 2559*x^3 + 1402*x^4 + 579*x^5 + 58*x^6 + 4*x^7 + 2*x^8 - x^9) / ((1 - x)^6*(1 + x)^4) - _Colin Barker_, Nov 10 2018.
%e Some solutions for n=6:
%e .10....7....1....1....2....8....2....0....0....2....3....3...11....1...11....8
%e ..0...10....6....6....8....0....6....4...12....9....4....0....2....9....1....3
%e ..1...11....7....9....0...11...10....7....6....1...11...12....3....8....5...11
%e .10....1....0....1....9....7....0...12....6...12....8....4...11....4....0....3
%e ..8....9....9...10....4....1...10....3...10...11....0....2....1...12....7....1
%e ..0....1....1....5....6....2...12...12....2....8...11....7....3....3...11....8
%Y Row 5 of A249982.
%K nonn
%O 1,1
%A _R. H. Hardin_, Nov 10 2014
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