A195522 T(n,k) = Number of lower triangles of an n X n -k..k array with all row and column sums zero.

1, 1, 1, 1, 1, 3, 1, 1, 5, 15, 1, 1, 7, 65, 199, 1, 1, 9, 175, 3753, 6247, 1, 1, 11, 369, 27267, 860017, 505623, 1, 1, 13, 671, 121367, 23663523, 839301197, 105997283, 1, 1, 15, 1105, 401565, 286168923, 122092290831, 3535646416019, 58923059879, 1, 1, 17

Offset: 1

Author

R. H. Hardin, Sep 20 2011

Keywords

• nonn
• tabl

Comments

Table starts

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

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

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

...15.....65......175.......369........671........1105........1695....2465.3439

..199...3753....27267....121367.....401565.....1089411.....2563933.5423365

.6247.860017.23663523.286168923.2106810049.11131321791.46387885537

Examples

			Some solutions for n=5 k=6
..0..........0..........0..........0..........0..........0..........0
..0.0.......-2.2........6-6.......-1.1........5-5.......-4.4.......-4.4
.-1.3-2.....-6.0.6.....-6.6.0.....-1.5-4.....-6.4.2......3-6.3.....-4.1.3
..6-3-2-1....4-4-4.4....5.3-5-3....0-5.3.2....0.4-3-1...-5.5.1-1....5-2-4.1
.-5.0.4.1.0..4.2-2-4.0.-5-3.5.3.0..2-1.1-2.0..1-3.1.1.0..6-3-4.1.0..3-3.1-1.0
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..75

Crossrefs

Row 4 is A005917(n+1).

Formula

Empirical for rows:

T(2,k) = 1

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

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

T(5,k) = (643/45)*k^6 + (643/15)*k^5 + (2165/36)*k^4 + (293/6)*k^3 + (4423/180)*k^2 + (73/10)*k + 1

T(6,k) = (7389349/90720)*k^10 + (7389349/18144)*k^9 + (836251/864)*k^8 + (4318165/3024)*k^7 + (6254923/4320)*k^6 + (4563293/4320)*k^5 + (10247161/18144)*k^4 + (249983/1134)*k^3 + (21959/360)*k^2 + (3469/315)*k + 1