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A200196 Number of -n..n arrays x(0..6) of 7 elements with zero sum, adjacent elements differing by more than one, and elements alternately increasing and decreasing.

%I A200196 #7 Jul 22 2025 15:44:14
%S A200196 0,104,1534,9856,40632,127800,334278,765598,1585416,3034396,5450616,
%T A200196 9293800,15170448,23863548,36362438,53897896,77976766,110422568,
%U A200196 153414642,209534448,281809258,373763982,489469484,633600106,811486280
%N A200196 Number of -n..n arrays x(0..6) of 7 elements with zero sum, adjacent elements differing by more than one, and elements alternately increasing and decreasing.
%C A200196 Row 7 of A200192
%H A200196 R. H. Hardin, <a href="/A200196/b200196.txt">Table of n, a(n) for n = 1..200</a>
%F A200196 Empirical: a(n) = 2*a(n-1) -a(n-3) -a(n-5) +a(n-6) -2*a(n-7) +2*a(n-8) +a(n-9) -a(n-13) -2*a(n-14) +2*a(n-15) -a(n-16) +a(n-17) +a(n-19) -2*a(n-21) +a(n-22)
%e A200196 Some solutions for n=5
%e A200196 .-3....1...-2....0...-2...-3....0...-1....3...-1...-1...-1....2...-4...-5...-2
%e A200196 ..2...-1....0....3....5....4....3...-3...-1....4....1...-4....4....0....0...-5
%e A200196 .-5....4...-2...-4...-4...-4...-3....4....2...-4...-4....3...-4...-3...-2....3
%e A200196 ..3...-4....5....5....1....5....1...-1...-3....4....3...-2...-1....5....3....1
%e A200196 .-3....2...-5...-5...-1...-2...-2....3....1...-3...-4....4...-4....1...-1....4
%e A200196 ..5...-2....3....5....2....5....2...-2...-4....5....4...-5....4....3....4...-3
%e A200196 ..1....0....1...-4...-1...-5...-1....0....2...-5....1....5...-1...-2....1....2
%K A200196 nonn
%O A200196 1,2
%A A200196 _R. H. Hardin_ Nov 14 2011