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

1,1

Comments

Row 5 of A200057.

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).

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

Example

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

Crossrefs

Cf. A200057.

Sequence in context: A297435 A281058 A152390 * A183470 A281051 A006737

Adjacent sequences: A200056 A200057 A200058 * A200060 A200061 A200062

Keyword

nonn

Author

R. H. Hardin, Nov 13 2011

Status

approved