A202256 Number of zero-sum -n..n arrays of 6 elements with adjacent element differences also in -n..n.

33, 387, 2003, 6963, 18841, 43293, 88301, 164873, 287151, 473293, 745359, 1130441, 1660283, 2372685, 3310839, 4525059, 6071723, 8015439, 10427561, 13388757, 16987109, 21321159, 26497455, 32634197, 39858185, 48309035, 58135563, 69500619

Offset: 1

Author

R. H. Hardin Dec 14 2011

Keywords

• nonn

Comments

Row 6 of A202252

Examples

			Some solutions for n=7
..6...-7...-5...-5....2....6....2...-1...-1....0...-6...-4....5....1....1...-6
..0....0....1....2...-1....1...-3...-5...-2...-4...-5...-5....4....0....2...-7
.-3....4....2...-2....6....0...-1...-1....0....1....2...-2...-2...-3...-1...-1
.-3....6....1....3...-1...-3...-1....1....3....1....1....5...-6....1....3....4
.-1....2....3....0...-6...-1....1....4....0...-1....5....4...-4....1....1....6
..1...-5...-2....2....0...-3....2....2....0....3....3....2....3....0...-6....4
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..210

Formula

Empirical: a(n) = 2*a(n-2) +2*a(n-3) -3*a(n-5) -3*a(n-6) -2*a(n-7) +a(n-8) +4*a(n-9) +4*a(n-10) +a(n-11) -2*a(n-12) -3*a(n-13) -3*a(n-14) +2*a(n-16) +2*a(n-17) -a(n-19).

Empirical: G.f. -x*(-33 -387*x -1937*x^2 -6123*x^3 -14061*x^4 -25460*x^5 -37953*x^6 -47841*x^7 -51602*x^8 -47844*x^9 -37956*x^10 -25461*x^11 -14061*x^12 -6120*x^13 -1935*x^14 -387*x^15 -35*x^16 -x^17+x^18) / ( (x^2+1) *(x^4+x^3+x^2+x+1) *(1+x+x^2)^2 *(1+x)^3 *(x-1)^6 ). - R. J. Mathar, Dec 15 2011