%I #14 Mar 02 2018 14:13:48

%S 4,9,22,41,66,107,158,219,304,403,516,661,824,1005,1226,1469,1734,

%T 2047,2386,2751,3172,3623,4104,4649,5228,5841,6526,7249,8010,8851,

%U 9734,10659,11672,12731,13836,15037,16288,17589,18994,20453,21966,23591,25274,27015

%N Number of 0..n arrays x(0..3) of 4 elements with zero 3rd differences.

%C Row 4 of A200154.

%H R. H. Hardin, <a href="/A200155/b200155.txt">Table of n, a(n) for n = 1..200</a>

%F Empirical: a(n) = 2*a(n-1) - a(n-2) + 2*a(n-3) - 4*a(n-4) + 2*a(n-5) - a(n-6) + 2*a(n-7) - a(n-8).

%F Empirical g.f.: x*(4 + x + 8*x^2 - 2*x^3 + 4*x^4 + 2*x^6 - x^7) / ((1 - x)^4*(1 + x + x^2)^2). - _Colin Barker_, Mar 02 2018

%e Some solutions for n=6:

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

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

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

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

%Y Cf. A200154.

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 13 2011