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A199913 Number of -n..n arrays x(0..5) of 6 elements with zero sum, and adjacent elements not equal modulo three (with -1 modulo 3 = 2).

%I A199913 #7 Jun 02 2025 05:25:39
%S A199913 32,232,1312,5016,12872,29864,62776,114768,200520,335216,522160,
%T A199913 792880,1174320,1666712,2327312,3198184,4271544,5640984,7367048,
%U A199913 9427264,11963896,15059328,18668000,22994912,28147648,34047432,40977792,49074872
%N A199913 Number of -n..n arrays x(0..5) of 6 elements with zero sum, and adjacent elements not equal modulo three (with -1 modulo 3 = 2).
%C A199913 Row 6 of A199909
%H A199913 R. H. Hardin, <a href="/A199913/b199913.txt">Table of n, a(n) for n = 1..200</a>
%F A199913 Empirical: a(n) = 2*a(n-1) -a(n-2) +4*a(n-3) -8*a(n-4) +4*a(n-5) -6*a(n-6) +12*a(n-7) -6*a(n-8) +4*a(n-9) -8*a(n-10) +4*a(n-11) -a(n-12) +2*a(n-13) -a(n-14)
%e A199913 Some solutions for n=6
%e A199913 .-1....2....5...-1...-4...-5...-3....4....2...-1...-5....0...-2...-2...-5....3
%e A199913 .-5....3....4....1....6....2....1...-1...-5...-3....5....5....3....0....3....4
%e A199913 .-1....4....5...-4....1....1....2....0....5....4...-2....1...-2...-4...-2....0
%e A199913 ..0...-4...-3....3...-4....3....3...-4...-6...-4....0...-6....0....4....3...-1
%e A199913 ..1...-3...-5...-5....6...-1....1....6....1....3....5....4...-2...-4...-5...-5
%e A199913 ..6...-2...-6....6...-5....0...-4...-5....3....1...-3...-4....3....6....6...-1
%K A199913 nonn
%O A199913 1,1
%A A199913 _R. H. Hardin_ Nov 11 2011