A195523 Number of lower triangles of a 5 X 5 -n..n array with all row and column sums zero.

199, 3753, 27267, 121367, 401565, 1089411, 2563933, 5423365, 10557163, 19228309, 33165903, 54668043, 86714993, 133092639, 198526233, 288824425, 411033583, 573602401, 786556795, 1061685087, 1412733477, 1855611803, 2408609589

Offset: 1

Author

R. H. Hardin, Sep 20 2011

Keywords

• nonn

Comments

Row 5 of A195522.

Examples

			Some solutions for n=4:
..0..........0..........0..........0..........0..........0..........0
..0.0.......-2.2.......-3.3........0.0.......-3.3........3-3........3-3
..0-3.3.....-2.4-2.....-2-1.3......2-2.0......0-1.1.....-3.0.3......2.0-2
..0.3.0-3....2-2.4-4....4-1-4.1....0-1.2-1....1.0-1.0....4-1.1-4...-4-1.4.1
..0.0-3.3.0..2-4-2.4.0..1-1.1-1.0.-2.3-2.1.0..2-2.0.0.0.-4.4-4.4.0.-1.4-2-1.0
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..175

Crossrefs

Cf. A195522.

Formula

Empirical: a(n) = (643/45)*n^6 + (643/15)*n^5 + (2165/36)*n^4 + (293/6)*n^3 + (4423/180)*n^2 + (73/10)*n + 1.

Conjectures from Colin Barker, May 08 2018: (Start)

G.f.: x*(199 + 2360*x + 5175*x^2 + 2346*x^3 + 213*x^4 - 6*x^5 + x^6) / (1 - x)^7.

a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>7.

(End)