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

1,1

Comments

Row 3 of A202784.

Links

R. H. Hardin, Table of n, a(n) for n = 1..210

Robert Israel, Proof of empirical formula for A202785

Wikipedia, Ehrhart polynomial

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

Example

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

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

Crossrefs

Cf. A202784.

Sequence in context: A321941 A116343 A259473 * A255535 A034544 A248060

Adjacent sequences: A202782 A202783 A202784 * A202786 A202787 A202788

Keyword

nonn

Author

R. H. Hardin, Dec 24 2011

Status

approved