A188124 Number of strictly increasing arrangements of 5 nonzero numbers in -(n+3)..(n+3) with sum zero.

0, 4, 16, 42, 90, 172, 296, 482, 740, 1092, 1554, 2154, 2906, 3846, 4992, 6382, 8038, 10004, 12302, 14984, 18074, 21626, 25670, 30266, 35442, 41266, 47770, 55024, 63064, 71966, 81766, 92548, 104350, 117258, 131316, 146616, 163200, 181168, 200566

Offset

0,2

Comments

Row 5 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)-2*a(n-5)+2*a(n-6)+a(n-8)-2*a(n-10)+a(n-11) = 269/1728 +235*n^2/144 +161*n/96 +23*n^4/288 +83*n^3/144 +(-1)^n*(1/64-3*n/32) -2*(-1)^n*A130815(n+2)/27 +A057077(n+1)/8.

Empirical: G.f. -2*x*(2+4*x+5*x^2+5*x^3+4*x^4+x^5+2*x^6) / ( (x^2+1)*(1+x+x^2)*(1+x)^2*(x-1)^5 ). - R. J. Mathar, Mar 21 2011

Example

4*x + 16*x^2 + 42*x^3 + 90*x^4 + 172*x^5 + 296*x^6 + 482*x^7 + 740*x^8 + ...
Some solutions for n=6
.-7...-7...-6...-7...-8...-8...-4...-9...-7...-5...-6...-4...-6...-9...-7...-5
.-5...-5...-4...-6...-6...-2...-3...-5...-5...-4...-3...-3...-3...-5...-4...-3
..1....2....2....2....1...-1...-2....1...-4...-2...-2...-2....1....2...-2....1
..5....3....3....5....4....4....4....5....7....4....4....1....2....5....6....3
..6....7....5....6....9....7....5....8....9....7....7....8....6....7....7....4

Prog

(PARI) {a(n) = local(v, c, m); m = n+3; forvec( v = vector( 5, i, [-m, m]), if( 0==prod( k=1, 5, v[k]), next); if( 0==sum( k=1, 5, v[k]), c++), 2); c} /* Michael Somos, Apr 11 2011 */

Crossrefs

Sequence in context: A018828 A323847 A114211 * A344857 A190090 A227012

Adjacent sequences: A188121 A188122 A188123 * A188125 A188126 A188127

Keyword

nonn

Author

R. H. Hardin, Mar 21 2011

Status

approved