A199945 Number of -n..n arrays x(0..3) of 4 elements with zeroth through 3rd differences all nonzero.

2, 104, 660, 2474, 6604, 14696, 28490, 50448, 83092, 129642, 193292, 278240, 388258, 528328, 703140, 918330, 1179228, 1492584, 1864202, 2301584, 2811588, 3402266, 4081084, 4857344, 5738882, 6735720, 7856884, 9112842, 10513196, 12069800

Offset

1,1

Comments

Row 4 of A199943.

Links

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

Formula

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

Empirical g.f.: 2*x*(1 + 51*x + 276*x^2 + 803*x^3 + 1408*x^4 + 1731*x^5 + 1436*x^6 + 825*x^7 + 303*x^8 + 78*x^9) / ((1 - x)^5*(1 + x)^2*(1 + x + x^2)^2). - Colin Barker, May 17 2018

Example

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

Crossrefs

Cf. A199943.

Sequence in context: A246775 A281053 A101530 * A346165 A265655 A001184

Adjacent sequences: A199942 A199943 A199944 * A199946 A199947 A199948

Keyword

nonn

Author

R. H. Hardin, Nov 12 2011

Status

approved