A200555 Number 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

Offset: 1

Author

R. H. Hardin, Nov 19 2011

Keywords

• nonn

Comments

Row 3 of A200553.

Examples

			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
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..200

Crossrefs

Cf. A200553.

Formula

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