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, 243728, 267916

Offset

1,1

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

Example

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

Crossrefs

Row 5 of A188333.

Sequence in context: A392948 A243803 A203855 * A185718 A043414 A044178

Adjacent sequences: A188332 A188333 A188334 * A188336 A188337 A188338

Keyword

nonn

Author

R. H. Hardin, Mar 28 2011

Status

approved