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A188123 Number of strictly increasing arrangements of 4 nonzero numbers in -(n+2)..(n+2) with sum zero. 1
1, 3, 8, 16, 31, 51, 80, 118, 167, 227, 302, 390, 495, 617, 758, 918, 1101, 1305, 1534, 1788, 2069, 2377, 2716, 3084, 3485, 3919, 4388, 4892, 5435, 6015, 6636, 7298, 8003, 8751, 9546, 10386, 11275, 12213, 13202, 14242, 15337, 16485, 17690, 18952, 20273, 21653 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Row 4 of A188122.

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..200

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

Sequence in context: A293358 A227265 A068039 * A081661 A005103 A001978

Adjacent sequences:  A188120 A188121 A188122 * A188124 A188125 A188126

KEYWORD

nonn

AUTHOR

R. H. Hardin Mar 21 2011

STATUS

approved

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Last modified November 21 17:44 EST 2017. Contains 295004 sequences.