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

1,1

Comments

Row 5 of A195522.

Links

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

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)

Example

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

Crossrefs

Cf. A195522.

Sequence in context: A324628 A216346 A289819 * A163712 A069244 A052355

Adjacent sequences: A195520 A195521 A195522 * A195524 A195525 A195526

Keyword

nonn

Author

R. H. Hardin, Sep 20 2011

Status

approved