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A188124 Number of strictly increasing arrangements of 5 nonzero numbers in -(n+3)..(n+3) with sum zero. 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Row 5 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)-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: A056373 A018828 A114211 * A190090 A227012 A034131

Adjacent sequences:  A188121 A188122 A188123 * A188125 A188126 A188127

KEYWORD

nonn

AUTHOR

R. H. Hardin, Mar 21 2011

STATUS

approved

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Last modified November 21 13:53 EST 2017. Contains 295001 sequences.