A199911 Number of -n..n arrays x(0..3) of 4 elements with zero sum, and adjacent elements not equal modulo three (with -1 modulo 3 = 2).

8, 24, 72, 152, 256, 448, 680, 952, 1384, 1848, 2368, 3136, 3912, 4760, 5960, 7128, 8384, 10112, 11752, 13496, 15848, 18040, 20352, 23424, 26248, 29208, 33096, 36632, 40320, 45120, 49448, 53944, 59752, 64952, 70336, 77248, 83400, 89752, 97864

Offset: 1

Author

R. H. Hardin, Nov 11 2011

Keywords

• nonn

Comments

Row 4 of A199909.

Examples

			Some solutions for n=6:
..0....0....0....2...-4...-5....1...-4...-4...-1...-3....5...-6....3....4....0
.-5....4....1...-3....3....0....2....3....6....0...-4...-5....1...-5....5...-2
..3...-3....5...-2....1....5...-5...-2....4...-2....6...-1....3....6...-5...-1
..2...-1...-6....3....0....0....2....3...-6....3....1....1....2...-4...-4....3
		

Links

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

Crossrefs

Cf. A199909.

Formula

Empirical: a(n) = a(n-1) +3*a(n-3) -3*a(n-4) -3*a(n-6) +3*a(n-7) +a(n-9) -a(n-10).

Empirical g.f.: 8*x*(1 + x)*(1 + x^2)*(1 + x + 4*x^2 + x^3 + x^4) / ((1 - x)^4*(1 + x + x^2)^3). - Colin Barker, May 17 2018