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

14, 76, 200, 446, 836, 1368, 2134, 3140, 4368, 5942, 7852, 10064, 12734, 15836, 19320, 23374, 27956, 33000, 38726, 45076, 51968, 59654, 68060, 77088, 87022, 97772, 109224, 121694, 135076, 149240, 164534, 180836, 198000, 216406, 235916, 256368, 278174, 301180, 325208

Offset: 1

Author

R. H. Hardin, Nov 19 2011

Keywords

• nonn
• changed

Examples

			Some solutions for n=3:
.-2....2....2...-1....2...-3...-2...-2....1...-3....0...-1....1....2...-2....2
..1...-3...-2....0...-1....3...-1....1....0....3...-1...-1...-2...-2...-1....1
..2....1....0...-1....0....2....3...-2....1...-1....2....1....0...-3....2...-3
.-1....0....0....2...-1...-2....0....3...-2....1...-1....1....1....3....1....0
		

Links

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

Crossrefs

Row 2 of A200553.

Formula

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).

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