OFFSET
0,2
COMMENTS
Row 4 of A188122.
LINKS
R. H. Hardin, Table of n, a(n) for n = 0..200 (corrected by R. H. Hardin, Jan 19 2019)
FORMULA
Empirical: a(n)=2*a(n-1)-a(n-3)-a(n-4)+2*a(n-6)-a(n-7) = 35/36 +2*n^2/3 +7*n/6 +2*n^3/9 +(-1)^n/4 -2*A049347(n)/9.
Empirical: G.f. -x*(-3-2*x-2*x^3-2*x^5+x^6) / ( (1+x)*(1+x+x^2)*(x-1)^4 ). - R. J. Mathar, Mar 21 2011
Empirical: a(n) = 1/108*(8*sqrt(3)*sin((2*Pi*n)/3) + 3*(2*n*(4*n*(n+3)+21) + 9*i*sin(Pi*n) + 35) - 24*cos((2*Pi*n)/3) + 27*cos(Pi*n)). - Alexander R. Povolotsky, Mar 21 2011
EXAMPLE
Some solutions for n=6
.-6...-7...-8...-8...-5...-7...-6...-6...-7...-5...-8...-4...-5...-7...-7...-4
.-1...-2...-5...-2...-4...-2...-4...-4...-6...-4....1...-3...-2...-6...-3...-3
..3....4....5....2....2....1....4....3....6....4....2....3...-1....5....3....2
..4....5....8....8....7....8....6....7....7....5....5....4....8....8....7....5
a(0) = 1 with unique solution [-2, -1, 1, 2]. - Michael Somos, Apr 11 2011
PROG
(PARI) {a(n) = local(v, c, m); m = n+2; forvec( v = vector( 4, i, [-m, m]), if( 0==prod( k=1, 4, v[k]), next); if( 0==sum( k=1, 4, v[k]), c++), 2); c} /* Michael Somos, Apr 11 2011 */
CROSSREFS
KEYWORD
nonn
AUTHOR
R. H. Hardin Mar 21 2011
STATUS
approved