A200205 Number of -n..n arrays x(0..3) of 4 elements with zero sum and nonzero second and third differences.

12, 68, 186, 422, 798, 1316, 2064, 3048, 4254, 5802, 7682, 9864, 12500, 15564, 19010, 23022, 27558, 32556, 38232, 44528, 51366, 58994, 67338, 76304, 86172, 96852, 108234, 120630, 133934, 148020, 163232, 179448, 196526, 214842, 234258, 254616

Offset

1,1

Comments

Row 1 of A200204.

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.: 2*x*(6 + 22*x + 31*x^2 + 47*x^3 + 26*x^4 + 9*x^5 + 3*x^6) / ((1 - x)^4*(1 + x + x^2)^2). - Colin Barker, May 20 2018

Example

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

Crossrefs

Cf. A200204.

Sequence in context: A199415 A200204 A289384 * A059585 A213547 A050484

Adjacent sequences: A200202 A200203 A200204 * A200206 A200207 A200208

Keyword

nonn

Author

R. H. Hardin, Nov 14 2011

Status

approved