A200456 Number of -n..n arrays x(0..3) of 4 elements with zero sum and nonzero first and second differences.

4, 44, 142, 342, 678, 1148, 1832, 2744, 3874, 5334, 7114, 9192, 11708, 14644, 17962, 21826, 26206, 31044, 36544, 42660, 49310, 56734, 64866, 73616, 83256, 93696, 104834, 116970, 130006, 143824, 158748, 174668, 191446, 209446, 228542, 248572

Offset: 1

Author

R. H. Hardin, Nov 18 2011

Keywords

• nonn

Comments

Row 2 of A200454.

Examples

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

Links

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

Crossrefs

Cf. A200454.

Formula

Empirical: a(n) = a(n-1) +2*a(n-3) -2*a(n-4) +a(n-5) -2*a(n-6) +a(n-7) -2*a(n-8) +2*a(n-9) +a(n-11) -a(n-12).

Empirical g.f.: 2*(1 + x)*(2 + 18*x + 31*x^2 + 65*x^3 + 63*x^4 + 72*x^5 + 52*x^6 + 39*x^7 + 9*x^8 + 9*x^9) / ((1 - x)^4*(1 + x + x^2)^2*(1 + x + x^2 + x^3 + x^4)). - Colin Barker, May 21 2018