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A200083 Number of 0..n arrays x(0..4) of 5 elements with zero 3rd differences.

%I A200083 #13 May 17 2018 13:40:20
%S A200083 2,3,8,17,26,43,64,89,122,163,208,269,334,407,496,597,702,831,968,
%T A200083 1117,1286,1471,1664,1889,2122,2371,2648,2945,3250,3595,3952,4329,
%U A200083 4738,5171,5616,6109,6614,7143,7712,8309,8918,9583,10264,10973,11726,12511,13312
%N A200083 Number of 0..n arrays x(0..4) of 5 elements with zero 3rd differences.
%C A200083 Row 4 of A200082.
%H A200083 R. H. Hardin, <a href="/A200083/b200083.txt">Table of n, a(n) for n = 1..200</a>
%F A200083 Empirical: a(n) = a(n-1) +a(n-3) -a(n-5) +a(n-6) -2*a(n-7) +a(n-8) -a(n-9) +a(n-11) +a(n-13) -a(n-14).
%F A200083 Empirical g.f.: x*(2 + x + 5*x^2 + 7*x^3 + 6*x^4 + 11*x^5 + 5*x^6 + 8*x^7 + 3*x^8 + x^9 + 2*x^10 + x^11 + x^12 - x^13) / ((1 - x)^4*(1 + x)^2*(1 - x + x^2)*(1 + x^2)*(1 + x + x^2)^2). - _Colin Barker_, May 17 2018
%e A200083 Some solutions for n=6:
%e A200083 ..2....1....2....3....0....4....0....5....0....6....6....3....6....0....4....3
%e A200083 ..3....3....4....4....4....4....0....6....3....2....3....3....3....1....3....5
%e A200083 ..3....4....5....4....6....4....0....6....4....0....2....3....1....2....2....6
%e A200083 ..2....4....5....3....6....4....0....5....3....0....3....3....0....3....1....6
%e A200083 ..0....3....4....1....4....4....0....3....0....2....6....3....0....4....0....5
%Y A200083 Cf. A200082.
%K A200083 nonn
%O A200083 1,1
%A A200083 _R. H. Hardin_, Nov 13 2011