A250230 - OEIS

%I #8 Nov 12 2018 14:38:52

%S 8,27,52,89,132,187,248,321,400,491,588,697,812,939,1072,1217,1368,

%T 1531,1700,1881,2068,2267,2472,2689,2912,3147,3388,3641,3900,4171,

%U 4448,4737,5032,5339,5652,5977,6308,6651,7000,7361,7728,8107,8492,8889,9292,9707

%N Number of length 3+1 0..n arrays with the sum of the cubes of adjacent differences multiplied by some arrangement of +-1 equal to zero.

%H R. H. Hardin, <a href="/A250230/b250230.txt">Table of n, a(n) for n = 1..145</a>

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

%F Empirical for n mod 2 = 0: a(n) = (9/2)*n^2 + 4*n + 1.

%F Empirical for n mod 2 = 1: a(n) = (9/2)*n^2 + 4*n - (1/2).

%F Empirical g.f.: x*(8 + 11*x - 2*x^2 + x^3) / ((1 - x)^3*(1 + x)). - _Colin Barker_, Nov 12 2018

%e Some solutions for n=6:

%e ..2....1....5....0....0....4....1....6....5....1....2....1....4....5....2....3

%e ..2....4....5....4....6....4....3....3....5....4....5....3....4....5....2....2

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

%e ..6....1....5....0....0....4....1....0....3....1....2....5....0....5....2....1

%Y Row 3 of A250229.

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 14 2014