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A200207 Number of -n..n arrays x(0..5) of 6 elements with zero sum and nonzero second and third differences 1

%I

%S 50,1042,6418,24542,70400,168054,352840,672632,1191380,1990668,

%T 3169582,4851400,7182342,10332674,14504130,19925886,26858060,35599134,

%U 46482708,59877540,76196440,95896240,119471266,147472836,180499346,219187302

%N Number of -n..n arrays x(0..5) of 6 elements with zero sum and nonzero second and third differences

%C Row 3 of A200204

%H R. H. Hardin, <a href="/A200207/b200207.txt">Table of n, a(n) for n = 1..200</a>

%F Empirical: a(n) = -a(n-1) -2*a(n-2) -2*a(n-3) -3*a(n-4) -2*a(n-5) -2*a(n-6) +3*a(n-9) +3*a(n-10) +6*a(n-11) +5*a(n-12) +7*a(n-13) +5*a(n-14) +7*a(n-15) +3*a(n-16) +5*a(n-17) +a(n-18) +3*a(n-19) -a(n-20) +a(n-21) -3*a(n-22) -a(n-23) -6*a(n-24) -4*a(n-25) -10*a(n-26) -8*a(n-27) -13*a(n-28) -11*a(n-29) -14*a(n-30) -10*a(n-31) -12*a(n-32) -6*a(n-33) -6*a(n-34) +a(n-36) +6*a(n-37) +7*a(n-38) +10*a(n-39) +10*a(n-40) +12*a(n-41) +11*a(n-42) +12*a(n-43) +12*a(n-44) +11*a(n-45) +12*a(n-46) +10*a(n-47) +10*a(n-48) +7*a(n-49) +6*a(n-50) +a(n-51) -6*a(n-53) -6*a(n-54) -12*a(n-55) -10*a(n-56) -14*a(n-57) -11*a(n-58) -13*a(n-59) -8*a(n-60) -10*a(n-61) -4*a(n-62) -6*a(n-63) -a(n-64) -3*a(n-65) +a(n-66) -a(n-67) +3*a(n-68) +a(n-69) +5*a(n-70) +3*a(n-71) +7*a(n-72) +5*a(n-73) +7*a(n-74) +5*a(n-75) +6*a(n-76) +3*a(n-77) +3*a(n-78) -2*a(n-81) -2*a(n-82) -3*a(n-83) -2*a(n-84) -2*a(n-85) -a(n-86) -a(n-87)

%e Some solutions for n=3

%e .-3....0...-2...-1....0...-3...-3....3....0...-2...-3...-1...-1....0...-2....3

%e .-3....1....3...-1....1...-2...-2....0...-1....2....2...-1...-3....1....1...-2

%e ..2....1....2....3....3....1....1...-1....2...-3...-2....3....3....0....3....3

%e ..0....3...-2...-2...-3....3....1....2....0...-1....3...-2...-2....1...-3....1

%e ..2...-3....0...-1...-2....1....0...-3....1....2....3....3....1...-3....0...-3

%e ..2...-2...-1....2....1....0....3...-1...-2....2...-3...-2....2....1....1...-2

%K nonn

%O 1,1

%A _R. H. Hardin_ Nov 14 2011

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