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

1,1

Comments

Row 5 of A188181

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

Example

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

Crossrefs

Sequence in context: A177721 A081268 A332595 * A183682 A243027 A242543

Adjacent sequences: A188180 A188181 A188182 * A188184 A188185 A188186

Keyword

nonn

Author

R. H. Hardin Mar 23 2011

Status

approved