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A200194 Number of -n..n arrays x(0..4) of 5 elements with zero sum, adjacent elements differing by more than one, and elements alternately increasing and decreasing.

%I A200194 #9 May 20 2018 11:33:27
%S A200194 0,24,144,506,1298,2794,5300,9220,14974,23094,34120,48712,67524,91346,
%T A200194 120950,157254,201146,253672,315838,388820,473738,571896,684534,
%U A200194 813084,958900,1123544,1308488,1515422,1745934,2001842,2284852,2596912,2939842
%N A200194 Number of -n..n arrays x(0..4) of 5 elements with zero sum, adjacent elements differing by more than one, and elements alternately increasing and decreasing.
%C A200194 Row 5 of A200192.
%H A200194 R. H. Hardin, <a href="/A200194/b200194.txt">Table of n, a(n) for n = 1..200</a>
%F A200194 Empirical: a(n) = 2*a(n-1) -a(n-3) -2*a(n-5) +2*a(n-6) +a(n-8) -2*a(n-10) +a(n-11).
%F A200194 Empirical g.f.: 2*x^2*(12 + 48*x + 109*x^2 + 155*x^3 + 171*x^4 + 133*x^5 + 79*x^6 + 26*x^7 + 3*x^8) / ((1 - x)^5*(1 + x)^2*(1 + x^2)*(1 + x + x^2)). - _Colin Barker_, May 20 2018
%e A200194 Some solutions for n=5:
%e A200194 ..0...-2...-3...-5...-2...-2...-4...-4....0....0....2....2...-5....1...-4....1
%e A200194 .-3....2....4....4....2....5....2....1...-3...-2...-2...-4....4...-2....3...-4
%e A200194 ..4...-4....0....0....0...-2...-5...-1....5....2....4....3...-3....2...-1....3
%e A200194 .-3....4....2....3....3....4....5....3...-5...-5...-5...-5....4...-4....4...-2
%e A200194 ..2....0...-3...-2...-3...-5....2....1....3....5....1....4....0....3...-2....2
%Y A200194 Cf. A200192.
%K A200194 nonn
%O A200194 1,2
%A A200194 _R. H. Hardin_, Nov 14 2011