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

Author

R. H. Hardin Nov 11 2011

Keywords

• nonn
• tabl

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

Examples

			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
		

Links

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

Crossrefs

Column 1 is A136029(n+1)

Row 3 is A082111

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