A188182 Number of strictly increasing arrangements of 4 numbers in -(n+2)..(n+2) with sum zero

5, 12, 24, 43, 69, 104, 150, 207, 277, 362, 462, 579, 715, 870, 1046, 1245, 1467, 1714, 1988, 2289, 2619, 2980, 3372, 3797, 4257, 4752, 5284, 5855, 6465, 7116, 7810, 8547, 9329, 10158, 11034, 11959, 12935, 13962, 15042, 16177, 17367, 18614, 19920, 21285

Offset

1,1

Comments

Row 4 of A188181

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: a(n) = (n+1)*(4*n^2+17*n+22)/18 -2 *A049347(n)/9; g.f. -x*(-5+3*x-3*x^2+3*x^3-3*x^4+x^5) / ( (1+x+x^2)*(x-1)^4 ). - R. J. Mathar, Mar 26 2011

Example

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

Crossrefs

Sequence in context: A101425 A191831 A365540 * A187210 A299901 A126880

Adjacent sequences: A188179 A188180 A188181 * A188183 A188184 A188185

Keyword

nonn

Author

R. H. Hardin Mar 23 2011

Status

approved