A200059 Number of -n..n arrays x(0..4) of 5 elements with zero sum and elements alternately strictly increasing and strictly decreasing.

6, 68, 288, 840, 1948, 3914, 7074, 11862, 18732, 28244, 40970, 57598, 78816, 105444, 138284, 178282, 226362, 283598, 351026, 429852, 521230, 626492, 746910, 883944, 1038982, 1213616, 1409348, 1627896, 1870884, 2140158, 2437454, 2764750, 3123900

Offset: 1

Author

R. H. Hardin, Nov 13 2011

Keywords

• nonn

Comments

Row 5 of A200057.

Examples

			Some solutions for n=6:
..1...-1....3...-6...-4...-1....1....4....6...-3....5...-1....1....1....1...-2
..0....2...-6....2....3...-5....2...-6...-1...-5...-6....2...-1....5...-2....6
..1...-2....4...-3...-3....5...-6....3....3....5....6...-4....4...-2....2...-5
.-3....5...-5....4....4...-1....4...-3...-5....1...-4....2...-3...-1...-5....1
..1...-4....4....3....0....2...-1....2...-3....2...-1....1...-1...-3....4....0
		

Links

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

Crossrefs

Cf. A200057.

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*(3 + 28*x + 76*x^2 + 135*x^3 + 168*x^4 + 159*x^5 + 105*x^6 + 51*x^7 + 10*x^8 + x^9) / ((1 - x)^5*(1 + x)^2*(1 + x^2)*(1 + x + x^2)). - Colin Barker, May 17 2018