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

1,3

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

Links

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

Example

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

Crossrefs

Column 1 is twice A077419 for n>1

Row 3 is twice A171769

Sequence in context: A115237 A105542 A208907 * A136600 A136672 A097750

Adjacent sequences: A200054 A200055 A200056 * A200058 A200059 A200060

Keyword

nonn,tabl

Author

R. H. Hardin Nov 13 2011

Status

approved