A202785 Number of 3 X 3 0..n arrays with row and column sums equal.

14, 87, 340, 1001, 2442, 5215, 10088, 18081, 30502, 48983, 75516, 112489, 162722, 229503, 316624, 428417, 569790, 746263, 964004, 1229865, 1551418, 1936991, 2395704, 2937505, 3573206, 4314519, 5174092, 6165545, 7303506, 8603647

Offset: 1

Author

R. H. Hardin, Dec 24 2011

Keywords

• nonn

Comments

Row 3 of A202784.

Examples

			Some solutions for n=7:
..3..2..1....3..5..5....0..6..2....0..7..5....4..2..1....5..6..0....1..6..1
..2..0..4....5..6..2....2..1..5....6..1..5....3..2..2....0..4..7....5..2..1
..1..4..1....5..2..6....6..1..1....6..4..2....0..3..4....6..1..4....2..0..6
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..210
• Robert Israel, Proof of empirical formula for A202785
• Wikipedia, Ehrhart polynomial

Crossrefs

Cf. A202784.

Programs

Maple

seq((3/10)*n^5 + (3/2)*n^4 + (7/2)*n^3 + (9/2)*n^2 + (16/5)*n + 1, n=1..30); # Robert Israel, May 02 2019

Formula

Empirical: a(n) = (3/10)*n^5 + (3/2)*n^4 + (7/2)*n^3 + (9/2)*n^2 + (16/5)*n + 1.

Conjectures from Colin Barker, Jun 01 2018: (Start)

G.f.: x*(7 - 2*x + x^2)*(2 + x + 4*x^2 - x^3) / (1 - x)^6.

a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n>6.

(End)

Empirical formula verified (see link): Robert Israel, May 02 2019