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Number of -n..n arrays x(0..4) of 5 elements with zero sum and nonzero second differences.
Row 3 of A200553.
Empirical: a(n) = a(n-1) +2*a(n-2) -3*a(n-4) -3*a(n-5) +3*a(n-6) +3*a(n-7) -2*a(n-9) -a(n-10) +a(n-11).
Empirical g.f.: 2*x*(13 + 127*x + 426*x^2 + 826*x^3 + 1046*x^4 + 912*x^5 + 544*x^6 + 205*x^7 + 37*x^8 + 4*x^9) / ((1 - x)^5*(1 + x)^2*(1 + x + x^2)^2). - Colin Barker, May 21 2018
Some solutions for n=3:
Cf. A200553.
R. H. Hardin , Nov 19 2011
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_R. H. Hardin (rhhardin(AT)att.net) _ Nov 19 2011
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R. H. Hardin, <a href="/A200555/b200555.txt">Table of n, a(n) for n = 1..200</a>
allocated for Ron HardinNumber of -n..n arrays x(0..4) of 5 elements with zero sum and nonzero second differences
26, 280, 1184, 3396, 7778, 15476, 27806, 46346, 72902, 109528, 158422, 222162, 303412, 405134, 530518, 683014, 866156, 1083954, 1340420, 1639900, 1986968, 2386470, 2843276, 3362828, 3950486, 4611980, 5353268, 6180592, 7100158, 8118840
1,1
Row 3 of A200553
Empirical: a(n) = a(n-1) +2*a(n-2) -3*a(n-4) -3*a(n-5) +3*a(n-6) +3*a(n-7) -2*a(n-9) -a(n-10) +a(n-11)
Some solutions for n=3
..3...-2...-3....0...-2....3...-2....2...-3...-2...-1....2....1....2...-2....3
..0...-3....2...-1....3...-1...-2....2....3....3....1....2....1...-2....1...-1
.-2....1....1....3....0....1....2...-1....0...-3...-2...-2...-2....2...-3...-3
..2....2....1...-2....1...-3....1...-2....2...-1....2....1...-1...-3....1....2
.-3....2...-1....0...-2....0....1...-1...-2....3....0...-3....1....1....3...-1
allocated
nonn
R. H. Hardin (rhhardin(AT)att.net) Nov 19 2011
approved
editing
allocated for Ron Hardin
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