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A199900 Number of -n..n arrays x(0..4) of 5 elements with zero sum, and adjacent elements not both strictly positive and not both strictly negative.

%I A199900 #9 May 16 2018 16:33:12
%S A199900 33,159,461,1043,2031,3573,5839,9021,13333,19011,26313,35519,46931,
%T A199900 60873,77691,97753,121449,149191,181413,218571,261143,309629,364551,
%U A199900 426453,495901,573483,659809,755511,861243,977681,1105523,1245489,1398321
%N A199900 Number of -n..n arrays x(0..4) of 5 elements with zero sum, and adjacent elements not both strictly positive and not both strictly negative.
%C A199900 Row 5 of A199898.
%H A199900 R. H. Hardin, <a href="/A199900/b199900.txt">Table of n, a(n) for n = 1..200</a>
%F A199900 Empirical: a(n) = (11/12)*n^4 + (49/6)*n^3 + (193/12)*n^2 + (41/6)*n + 1.
%F A199900 Conjectures from _Colin Barker_, May 16 2018: (Start)
%F A199900 G.f.: x*(33 - 6*x - 4*x^2 - 2*x^3 + x^4) / (1 - x)^5.
%F A199900 a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>5.
%F A199900 (End)
%e A199900 Some solutions for n=6:
%e A199900 .-4...-2....0....2....0....2....0....0...-5....2...-1...-2...-4....3...-6...-6
%e A199900 ..3....2....3...-4....1...-3...-3....6....5...-1....4....0....6...-6....1....6
%e A199900 .-1...-1...-5....0....0....3....6....0...-3....1...-3....5...-1....2...-1...-1
%e A199900 ..6....5....0...-2....5...-3...-3...-6....5...-5....5....0....1...-3....6....4
%e A199900 .-4...-4....2....4...-6....1....0....0...-2....3...-5...-3...-2....4....0...-3
%Y A199900 Cf. A199898.
%K A199900 nonn
%O A199900 1,1
%A A199900 _R. H. Hardin_, Nov 11 2011