A200057 T(n,k)=Number of -k..k arrays x(0..n-1) of n elements with zero sum and elements alternately strictly increasing and strictly decreasing.

1, 1, 2, 1, 4, 4, 1, 6, 10, 4, 1, 8, 22, 26, 6, 1, 10, 36, 78, 68, 10, 1, 12, 56, 172, 288, 178, 14, 1, 14, 78, 324, 840, 1098, 472, 22, 1, 16, 106, 546, 1948, 4172, 4224, 1276, 34, 1, 18, 136, 850, 3914, 11962, 20978, 16432, 3462, 52, 1, 20, 172, 1252, 7074, 28554, 74338

Offset: 1

Author

R. H. Hardin Nov 13 2011

Keywords

• nonn
• tabl

Comments

Table starts

..1....1......1.......1........1........1.........1..........1..........1

..2....4......6.......8.......10.......12........14.........16.........18

..4...10.....22......36.......56.......78.......106........136........172

..4...26.....78.....172......324......546.......850.......1252.......1764

..6...68....288.....840.....1948.....3914......7074......11862......18732

.10..178...1098....4172....11962....28554.....59910.....114232.....202314

.14..472...4224...20978....74338...211242....514168....1115572....2215290

.22.1276..16432..106674...466548..1577878...4453946...10995240...24477966

.34.3462..64310..545698..2947742.11867186..38855488..109147062..272432422

.52.9496.253692.2811236.18746754.89815404.341052122.1090022120.3050199016

Examples

			Some solutions for n=7 k=6
..3....0...-2....1....0...-3....0....0...-3....0...-3...-3....3...-3....0...-6
.-1...-3...-6....0...-1....6....2....5...-6....5...-6....0...-3...-2...-4....3
..0....5....6....3....6...-3...-2...-5....4...-5....3...-1....3...-3....4...-2
.-4....2...-5...-4...-3...-2....1....6...-5....6...-3....4...-5....1...-6....5
..4....4....1...-1...-1...-4...-5...-3....5...-3....6...-1....4...-1....6....1
.-3...-6....0...-3...-6....6....4....1...-1....2...-3....3...-3....6...-5....3
..1...-2....6....4....5....0....0...-4....6...-5....6...-2....1....2....5...-4
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..871

Crossrefs

Column 1 is twice A077419 for n>1

Row 3 is twice A171769