A202512 Number of zero-sum -n..n arrays of 4 elements with first through third differences also in -n..n.

1, 15, 29, 75, 115, 217, 297, 479, 609, 887, 1091, 1493, 1765, 2315, 2689, 3399, 3875, 4777, 5373, 6491, 7213, 8555, 9439, 11041, 12061, 13947, 15157, 17331, 18719, 21221, 22809, 25663, 27453, 30659, 32699, 36301, 38545, 42567, 45089, 49527, 52303, 57205

Offset

1,2

Comments

Row 4 of A202511.

Links

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

Formula

Empirical: a(n) = -a(n-1) +2*a(n-3) +4*a(n-4) +2*a(n-5) -a(n-6) -5*a(n-7) -5*a(n-8) -a(n-9) +2*a(n-10) +4*a(n-11) +2*a(n-12) -a(n-14) -a(n-15).

Empirical g.f.: x*(1 + 16*x + 44*x^2 + 102*x^3 + 156*x^4 + 212*x^5 + 219*x^6 + 208*x^7 + 153*x^8 + 100*x^9 + 46*x^10 + 18*x^11 + 2*x^12 - x^14) / ((1 - x)^4*(1 + x)^3*(1 + x^2)^2*(1 + x + x^2)^2). - Colin Barker, Jun 01 2018

Example

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

Crossrefs

Cf. A202511.

Sequence in context: A211324 A354163 A146427 * A014095 A192356 A350468

Adjacent sequences: A202509 A202510 A202511 * A202513 A202514 A202515

Keyword

nonn

Author

R. H. Hardin, Dec 20 2011

Status

approved