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

1,6

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

Links

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

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

Example

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

Crossrefs

Row 4 is A005917(n+1).

Sequence in context: A341470 A293796 A195892 * A273169 A273167 A324284

Adjacent sequences: A195519 A195520 A195521 * A195523 A195524 A195525

Keyword

nonn,tabl

Author

R. H. Hardin, Sep 20 2011

Status

approved