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A200557 Number of -n..n arrays x(0..6) of 7 elements with zero sum and nonzero second differences.

%I A200557 #7 Jul 22 2025 15:52:31
%S A200557 142,4978,43698,211374,737460,2076774,5012084,10807826,21368704,
%T A200557 39388482,68614738,114064374,182196622,281328582,421889370,616590012,
%U A200557 881040966,1234022180,1697613488,2298081194,3066132222,4036964078,5251498784
%N A200557 Number of -n..n arrays x(0..6) of 7 elements with zero sum and nonzero second differences.
%C A200557 Row 5 of A200553
%H A200557 R. H. Hardin, <a href="/A200557/b200557.txt">Table of n, a(n) for n = 1..146</a>
%F A200557 Empirical: a(n) = 3*a(n-1) -6*a(n-2) +11*a(n-3) -16*a(n-4) +21*a(n-5) -24*a(n-6) +23*a(n-7) -19*a(n-8) +10*a(n-9) +a(n-10) -13*a(n-11) +25*a(n-12) -34*a(n-13) +40*a(n-14) -41*a(n-15) +37*a(n-16) -28*a(n-17) +14*a(n-18) +3*a(n-19) -20*a(n-20) +34*a(n-21) -42*a(n-22) +42*a(n-23) -34*a(n-24) +20*a(n-25) -3*a(n-26) -14*a(n-27) +28*a(n-28) -37*a(n-29) +41*a(n-30) -40*a(n-31) +34*a(n-32) -25*a(n-33) +13*a(n-34) -a(n-35) -10*a(n-36) +19*a(n-37) -23*a(n-38) +24*a(n-39) -21*a(n-40) +16*a(n-41) -11*a(n-42) +6*a(n-43) -3*a(n-44) +a(n-45)
%e A200557 Some solutions for n=3
%e A200557 .-3....2....0...-1...-1....0....0...-1...-1....2....3....1....1...-2...-3....1
%e A200557 ..0...-3...-1....0...-3....0...-2....1...-3....2...-2...-1....3....2....3....2
%e A200557 .-3....0....0...-3....1....1...-2...-2....3...-2...-2....1....0....0...-3...-1
%e A200557 ..3....0....2...-3....1...-3....3....0....0....0....0...-1....0...-3....2....3
%e A200557 ..3...-1....3....3....3....3....3...-1....3....1...-3...-1...-1....1....0...-2
%e A200557 .-2....2...-2....3...-1....2....1....1....0...-2....1....1...-3....2....3...-1
%e A200557 ..2....0...-2....1....0...-3...-3....2...-2...-1....3....0....0....0...-2...-2
%K A200557 nonn
%O A200557 1,1
%A A200557 _R. H. Hardin_ Nov 19 2011