A188183 Number of strictly increasing arrangements of 5 numbers in -(n+3)..(n+3) with sum zero.

12, 32, 73, 141, 252, 414, 649, 967, 1394, 1944, 2649, 3523, 4604, 5910, 7483, 9343, 11538, 14090, 17053, 20451, 24342, 28754, 33751, 39361, 45654, 52662, 60459, 69079, 78602, 89064, 100551, 113101, 126804, 141702, 157891, 175413, 194370, 214808

Offset: 1

Author

R. H. Hardin Mar 23 2011

Keywords

• nonn

Comments

Row 5 of A188181

Examples

			Some solutions for n=5
.-5...-8...-7...-8...-6...-4...-8...-6...-8...-5...-8...-7...-6...-6...-8...-7
.-3...-3...-4...-6...-2...-3...-7...-5...-2...-3...-2...-4...-5...-5...-1...-6
.-1...-2....0....0...-1...-1....4...-2....2...-1....1...-2....2...-3....1....1
..3....5....4....6....2....0....5....6....3....1....3....6....3....6....3....4
..6....8....7....8....7....8....6....7....5....8....6....7....6....8....5....8
		

Links

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

Formula

Empirical: a(n)=2*a(n-1)-a(n-3)-2*a(n-5)+2*a(n-6)+a(n-8)-2*a(n-10)+a(n-11).

Empirical: a(n) = 427*n^2/144 +155*n/32 +5501/1728+23*n^4/288 +115*n^3/144 -3*(-1)^n*n/32-15*(-1)^n/64 +A057077(n+1)/8 -2*A061347(n+1)/27; g.f. -x*(12 +8*x +9*x^2 +7*x^3 +2*x^4 +7*x^5 +2*x^6 +3*x^7 -2*x^8 -5*x^9 +3*x^10) / ( (x^2+1) *(1+x+x^2) *(1+x)^2 *(x-1)^5 ). - R. J. Mathar, Mar 26 2011