A201875 Number of zero-sum -n..n arrays of 4 elements with first and second differences also in -n..n.

3, 19, 45, 95, 173, 285, 431, 633, 879, 1183, 1557, 1999, 2509, 3117, 3803, 4581, 5471, 6463, 7557, 8791, 10137, 11609, 13235, 14997, 16895, 18975, 21201, 23587, 26169, 28921, 31843, 34989, 38315, 41835, 45593, 49555, 53721, 58153, 62799, 67673, 72827

Offset

1,1

Comments

Row 4 of A201873.

Links

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

Formula

Empirical: a(n) = a(n-1) +a(n-2) +a(n-3) -2*a(n-4) -2*a(n-5) +a(n-6) +a(n-7) +a(n-8) -a(n-9).

Empirical g.f.: (3 + 16*x + 23*x^2 + 28*x^3 + 20*x^4 + 16*x^5 + 3*x^6 + 2*x^7 - x^8) / ((1 - x)^4*(1 + x)*(1 + x + x^2)^2). - Colin Barker, Feb 15 2018

Example

Some solutions for n=11:
..0...-1....4...-7...-7...10...-1...-6...-9..-11....1....9....4...-8...-4....7
..0....5...-2...-4...-2...-1....1...-3....1...-3...-1....6...-4...-4....4....2
..2....0....1....5...-1...-3...-2....4....5....3....1...-4...-1....2....3...-6
.-2...-4...-3....6...10...-6....2....5....3...11...-1..-11....1...10...-3...-3

Crossrefs

Sequence in context: A146664 A028880 A162905 * A063553 A099007 A023280

Adjacent sequences: A201872 A201873 A201874 * A201876 A201877 A201878

Keyword

nonn

Author

R. H. Hardin, Dec 06 2011

Status

approved