A188335 Number of nondecreasing arrangements of 5 nonzero numbers in -(n+3)..(n+3) with sum zero.

40, 86, 166, 288, 472, 726, 1076, 1534, 2130, 2878, 3814, 4954, 6340, 7990, 9950, 12242, 14918, 18000, 21546, 25582, 30170, 35338, 41154, 47648, 54894, 62924, 71816, 81606, 92378, 104168, 117066, 131112, 146400, 162972, 180928, 200312, 221230

Offset: 1

Author

R. H. Hardin Mar 28 2011

Keywords

• nonn

Comments

Row 5 of A188333

Examples

			Some solutions for n=6
.-4...-7...-4...-7...-5...-9...-6...-7...-5...-7...-9...-5...-9...-5...-8...-6
.-3...-3...-3...-4...-5...-7...-6...-4...-4...-4...-5...-4...-3...-3...-3...-6
..1...-1...-3....2....1....1....2....2...-1....3....3....2....2....1...-2...-1
..3....4....4....3....2....6....2....4....4....4....3....3....5....1....5....4
..3....7....6....6....7....9....8....5....6....4....8....4....5....6....8....9
		

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: g.f. -2*x*(20 +3*x -3*x^2 -2*x^3 -9*x^4 +14*x^5 +2*x^6 +7*x^7 -4*x^8 -12*x^9 +7*x^10) / ( (x^2+1) *(1+x+x^2) *(1+x)^2 *(x-1)^5 ). a(n) = 23*n^4/288 +175*n^3/144 +985*n^2/144 +1601*n/96 +25265/1728 -(-1)^n*(3*n/32+27/64) -2*A061347(n+1)/27 -A057077(n+1)/8. - R. J. Mathar, Mar 28 2011