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

1,1

Comments

Row 4 of A200154.

Links

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

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

Example

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

Crossrefs

Cf. A200154.

Sequence in context: A158140 A290647 A105314 * A002835 A253289 A032288

Adjacent sequences: A200152 A200153 A200154 * A200156 A200157 A200158

Keyword

nonn

Author

R. H. Hardin, Nov 13 2011

Status

approved