A200155 Number of 0..n arrays x(0..3) of 4 elements with zero 3rd differences.

4, 9, 22, 41, 66, 107, 158, 219, 304, 403, 516, 661, 824, 1005, 1226, 1469, 1734, 2047, 2386, 2751, 3172, 3623, 4104, 4649, 5228, 5841, 6526, 7249, 8010, 8851, 9734, 10659, 11672, 12731, 13836, 15037, 16288, 17589, 18994, 20453, 21966, 23591, 25274, 27015

Offset: 1

Author

R. H. Hardin, Nov 13 2011

Keywords

• nonn

Comments

Row 4 of A200154.

Examples

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

Links

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

Crossrefs

Cf. A200154.

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.: x*(4 + x + 8*x^2 - 2*x^3 + 4*x^4 + 2*x^6 - x^7) / ((1 - x)^4*(1 + x + x^2)^2). - Colin Barker, Mar 02 2018