A199898 T(n,k)=Number of -k..k arrays x(0..n-1) of n elements with zero sum, and adjacent elements not both strictly positive and not both strictly negative

1, 1, 3, 1, 5, 7, 1, 7, 15, 15, 1, 9, 25, 49, 33, 1, 11, 37, 111, 159, 75, 1, 13, 51, 209, 461, 533, 171, 1, 15, 67, 351, 1043, 2035, 1783, 391, 1, 17, 85, 545, 2031, 5725, 8823, 6027, 899, 1, 19, 105, 799, 3573, 13363, 30199, 39053, 20437, 2077, 1, 21, 127, 1121, 5839

Offset

1,3

Comments

Table starts

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

....3.....5......7.......9.......11.......13........15........17.........19

....7....15.....25......37.......51.......67........85.......105........127

...15....49....111.....209......351......545.......799......1121.......1519

...33...159....461....1043.....2031.....3573......5839......9021......13333

...75...533...2035....5725....13363....27457.....51395.....89577.....147547

..171..1783...8823...30199....82555...193689....406575....783989....1413739

..391..6027..39053..164993...536967..1462859...3500269...7584081...15191479

..899.20437.172355..890299..3409609.10651367..28684325..68971571..151640029

.2077.69665.767425.4877477.22163661.80142549.245319361.661158741.1611184533

Links

R. H. Hardin, Table of n, a(n) for n = 1..1096

Formula

Empirical for rows:

T(1,k) = 1

T(2,k) = 2*k + 1

T(3,k) = k^2 + 5*k + 1

T(4,k) = (4/3)*k^3 + 6*k^2 + (20/3)*k + 1

T(5,k) = (11/12)*k^4 + (49/6)*k^3 + (193/12)*k^2 + (41/6)*k + 1

T(6,k) = (11/10)*k^5 + (55/6)*k^4 + (55/2)*k^3 + (173/6)*k^2 + (37/5)*k + 1

T(7,k) = (151/180)*k^6 + (163/15)*k^5 + (377/9)*k^4 + (395/6)*k^3 + (7429/180)*k^2 + (93/10)*k + 1

Example

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

Crossrefs

Column 1 is A136029(n+1)

Row 3 is A082111

Sequence in context: A193648 A221881 A201811 * A320904 A193844 A201552

Adjacent sequences: A199895 A199896 A199897 * A199899 A199900 A199901

Keyword

nonn,tabl

Author

R. H. Hardin Nov 11 2011

Status

approved