A200554 Number of -n..n arrays x(0..3) of 4 elements with zero sum and nonzero second differences.

14, 76, 200, 446, 836, 1368, 2134, 3140, 4368, 5942, 7852, 10064, 12734, 15836, 19320, 23374, 27956, 33000, 38726, 45076, 51968, 59654, 68060, 77088, 87022, 97772, 109224, 121694, 135076, 149240, 164534, 180836, 198000, 216406, 235916, 256368

Offset

1,1

Comments

Row 2 of A200553.

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*(7 + 24*x + 31*x^2 + 47*x^3 + 24*x^4 + 9*x^5 + 2*x^6) / ((1 - x)^4*(1 + x + x^2)^2). - Colin Barker, May 21 2018

Example

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

Crossrefs

Cf. A200553.

Sequence in context: A093567 A296996 A270704 * A152100 A173962 A200547

Adjacent sequences: A200551 A200552 A200553 * A200555 A200556 A200557

Keyword

nonn

Author

R. H. Hardin, Nov 19 2011

Status

approved