A199848 Number of -n..n arrays x(0..3) of 4 elements with zero sum and no element more than one greater than the previous.

11, 23, 42, 68, 103, 149, 206, 276, 361, 461, 578, 714, 869, 1045, 1244, 1466, 1713, 1987, 2288, 2618, 2979, 3371, 3796, 4256, 4751, 5283, 5854, 6464, 7115, 7809, 8546, 9328, 10157, 11033, 11958, 12934, 13961, 15041, 16176, 17366, 18613, 19919, 21284

Offset

1,1

Comments

Row 4 of A199847.

Links

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

Formula

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

Empirical g.f.: x*(11 - 10*x + 6*x^2 - 11*x^3 + 12*x^4 - 4*x^5) / ((1 - x)^4*(1 + x + x^2)). - Colin Barker, May 16 2018

Example

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

Crossrefs

Cf. A199847.

Sequence in context: A190797 A068842 A357364 * A352494 A228444 A191235

Adjacent sequences: A199845 A199846 A199847 * A199849 A199850 A199851

Keyword

nonn

Author

R. H. Hardin, Nov 11 2011

Status

approved