A200040 Number of -n..n arrays x(0..3) of 4 elements with sum zero and with zeroth through 3rd differences all nonzero.

2, 28, 84, 218, 444, 808, 1330, 2068, 2996, 4230, 5740, 7552, 9746, 12348, 15304, 18782, 22732, 27144, 32162, 37784, 43912, 50790, 58332, 66496, 75494, 85280, 95736, 107166, 119452, 132524, 146646, 161752, 177688, 194822, 213008, 232132, 252534

Offset

1,1

Comments

Row 4 of A200038.

Links

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

Formula

Empirical: a(n) = a(n-2) +2*a(n-3) -a(n-5) -a(n-6) -a(n-7) -a(n-8) +2*a(n-10) +a(n-11) -a(n-13).

Empirical g.f.: 2*x*(1 + 14*x + 41*x^2 + 93*x^3 + 152*x^4 + 212*x^5 + 240*x^6 + 243*x^7 + 191*x^8 + 138*x^9 + 79*x^10 + 36*x^11) / ((1 - x)^4*(1 + x)*(1 + x + x^2)^2*(1 + x + x^2 + x^3 + x^4)). - Colin Barker, May 17 2018

Example

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

Crossrefs

Cf. A200038.

Sequence in context: A156471 A329595 A138964 * A334696 A281201 A051958

Adjacent sequences: A200037 A200038 A200039 * A200041 A200042 A200043

Keyword

nonn

Author

R. H. Hardin, Nov 12 2011

Status

approved