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A200457 Number of -n..n arrays x(0..4) of 5 elements with zero sum and nonzero first and second differences.

%I A200457 #7 Jul 22 2025 15:50:14
%S A200457 6,144,728,2334,5720,12002,22276,38174,61290,93704,137374,194964,
%T A200457 268842,362092,477620,618954,789324,992970,1233412,1515270,1842742,
%U A200457 2220844,2654034,3148080,3707758,4339192,5047836,5840186,6721964,7700510,8781768
%N A200457 Number of -n..n arrays x(0..4) of 5 elements with zero sum and nonzero first and second differences.
%C A200457 Row 3 of A200454
%H A200457 R. H. Hardin, <a href="/A200457/b200457.txt">Table of n, a(n) for n = 1..200</a>
%F A200457 Empirical: a(n) = -a(n-1) +a(n-3) +2*a(n-4) +2*a(n-5) +a(n-6) -a(n-8) -a(n-9) -a(n-10) -2*a(n-11) -2*a(n-12) -2*a(n-13) -a(n-14) +a(n-15) +2*a(n-16) +2*a(n-17) +2*a(n-18) +a(n-19) +a(n-20) +a(n-21) -a(n-23) -2*a(n-24) -2*a(n-25) -a(n-26) +a(n-28) +a(n-29)
%e A200457 Some solutions for n=3
%e A200457 .-1....0...-2...-1....3....3...-1....1...-2...-2....1...-2...-2....3...-3....0
%e A200457 ..2...-2...-1....0...-2...-1....1...-3....1....1....3....0....3...-1....3...-2
%e A200457 .-2...-3....1...-2....0....3...-3....1...-1...-1...-3....1....1....2...-1....2
%e A200457 ..1....3....0....3....1...-3....3...-1....3....2....0...-1....0...-3....3...-3
%e A200457 ..0....2....2....0...-2...-2....0....2...-1....0...-1....2...-2...-1...-2....3
%K A200457 nonn
%O A200457 1,1
%A A200457 _R. H. Hardin_ Nov 18 2011