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A200554 Number of -n..n arrays x(0..3) of 4 elements with zero sum and nonzero second differences.

%I A200554 #12 Aug 24 2025 11:24:38
%S A200554 14,76,200,446,836,1368,2134,3140,4368,5942,7852,10064,12734,15836,
%T A200554 19320,23374,27956,33000,38726,45076,51968,59654,68060,77088,87022,
%U A200554 97772,109224,121694,135076,149240,164534,180836,198000,216406,235916,256368,278174,301180,325208
%N A200554 Number of -n..n arrays x(0..3) of 4 elements with zero sum and nonzero second differences.
%H A200554 R. H. Hardin, <a href="/A200554/b200554.txt">Table of n, a(n) for n = 1..200</a>
%F A200554 Empirical: a(n) = 2*a(n-1) -a(n-2) +2*a(n-3) -4*a(n-4) +2*a(n-5) -a(n-6) +2*a(n-7) -a(n-8).
%F A200554 Empirical g.f.: 2*x*(7 + 24*x + 31*x^2 + 47*x^3 + 24*x^4 + 9*x^5 + 2*x^6) / ((1 - x)^4*(1 + x + x^2)^2). - _Colin Barker_, May 21 2018
%e A200554 Some solutions for n=3:
%e A200554 .-2....2....2...-1....2...-3...-2...-2....1...-3....0...-1....1....2...-2....2
%e A200554 ..1...-3...-2....0...-1....3...-1....1....0....3...-1...-1...-2...-2...-1....1
%e A200554 ..2....1....0...-1....0....2....3...-2....1...-1....2....1....0...-3....2...-3
%e A200554 .-1....0....0....2...-1...-2....0....3...-2....1...-1....1....1....3....1....0
%Y A200554 Row 2 of A200553.
%K A200554 nonn,changed
%O A200554 1,1
%A A200554 _R. H. Hardin_, Nov 19 2011